MathMaster logo

MathMaster

  1. Home
  2. general
  3. a water pipe runs diagonally under a rectangular garden that is 7 feet longer than it is wide if the pipe is 13 feet long
Question

A water pipe runs diagonally under a rectangular garden that is 7 feet longer than it is wide. If the pipe is 13 feet long what are the dimensions of the garden

89

likes
445 views

Answer to a math question A water pipe runs diagonally under a rectangular garden that is 7 feet longer than it is wide. If the pipe is 13 feet long what are the dimensions of the garden

Expert avatar
Sigrid
4.5
111 Answers
1. Write the equation for the Pythagorean theorem:
w^2 + (w + 7)^2 = 13^2

2. Calculate the square of 13:
13^2 = 169

3. Expand the equation:
w^2 + (w + 7)^2 = 169

w^2 + (w^2 + 14w + 49) = 169

4. Combine like terms:
2w^2 + 14w + 49 = 169

5. Simplify and rearrange the equation:
2w^2 + 14w + 49 - 169 = 0

2w^2 + 14w - 120 = 0

6. Divide the entire equation by 2 to simplify:
w^2 + 7w - 60 = 0

7. Factor the quadratic equation:
(w + 12)(w - 5) = 0

8. Solve for w:
- Either w + 12 = 0 which gives w = -12 (not possible in this context, since width can't be negative)
- Or w - 5 = 0 which gives w = 5

9. Find the length:
- Length = w + 7 = 5 + 7 = 12

Therefore, the width is 5 feet and the length is 12 feet.

Frequently asked questions (FAQs)
What is the slope of a line passing through points (2, 3) and (-4, 5)?
+
Question: Given triangle ABC and triangle PQR, if angle A is congruent to angle P and side AB is congruent to side QR, can we conclude that triangle ABC is congruent to triangle PQR?
+
What fraction of 50 is 30?
+
New questions in Mathematics
calculate the following vector based on its base vectors a= -18i,26j
Derivative of x squared
(5u + 6)-(3u+2)=
3(2•1+3)4
If the midpoint of point A on the x=3 line and point B on the y=-2 line is C(-2,0), what is the sum of the ordinate of point A and the abscissa of point B?
A merchant can sell 20 electric shavers a day at a price of 25 each, but he can sell 30 if he sets a price of 20 for each electric shaver. Determine the demand equation, assuming it is linear. Consider (P= price, X= quantity demanded)
You mix a powder drug with a 4.5ml of liquid to get a reconstituted solution with a concentration of 250mg/ml. The prescribers order is for 500 mg . You will give what ml of the reconstituted solution
Your boss asks you to plan the sample size for a randomized, double-blind, controlled trial in the clinical development of a cure for irritable bowl disease. Current standard treatment shall be compared with a new treatment in this trial. The S3-guideline of AWM demonstrated a mean change of the summary score of the validated health related quality of life questionnaire at 8 weeks of 16 with standard deviation 23 under standard treatment. You quote the drop-out rate of 11% from literature (previous phase of clinical development). Your research yielded a clinically important effect of 4 that has been found to be the Minimal Clinically Important Difference (MCID). In order to demonstrate superiority of the new treatment over standard of care, you assume that the change in of the summary score of the validated health related quality of life questionnaire follows a normal distribution, and that the standard deviation is the same for both treatments. How many patientes would one need to recruit for the trial to demonstrate the clinically interesting difference between treatments at significance level 5% with 95% power?
Equine infectious anemia (EIA) is considered the main infectious disease in Brazilian equine farming, for which there is no effective vaccine or treatment. It is caused by a retrovirus of the genus Lentivirus, which affects horses, donkeys and mules and is transmitted in nature mainly by hematophagous insects of the genus Tabanidae. Researchers analyzed the records of 9,439 equids from Acre, submitted to the agar gel immunodiffusion test (AGID) for equine infectious anemia (EIA), between 1986 and 1996. Of these, 6199 tested positive for equine infectious anemia (EIA) . Knowing that the age of AIE-positive horses follows a Normal distribution with a mean of 5 years and a standard deviation of 1.5 years, determine the expected number of AIE-positive horses in the Acre sample that will be aged less than or equal to 3 years. ATTENTION: Provide the answer to exactly FOUR decimal places.
Given (3x+2)E [2;14] how much money (in soles) does Sophia have if numerically it is the greatest value of x?
(2m+3)(4m+3)=0
Find the complement and supplement angles of 73
Write the equation of the line that is parallel to y= 4x-7 and has a y- intercept at (0,5)
The mass of 120 molecules of X2C4 is 9127.2 amu. Identify the unknown atom, X, by finding the atomic mass. The atomic mass of C is 12.01 amu/atom
A house located within the city limits has a current market value of $325,000 according to a recent appraisal. The assessed value from the last county wide tax valuation is $272,475. The tax rate is $0.36 per hundred for the county and $0.72 per hundred for the city. What is the total annual property tax liability on the property? $2340 $3510 $1962 $2943
Consider a sample space S, and two events A and B such that P(A ∩ B) = 0.2, P(A ∪ B) = 0.6, P(B ∪ ̄A) = 0.8 (a) [0.5 points] Calculate P (A). (b) [0.5 points] Calculation P (B)
Two trains leave stations 294 miles apart at the same time and travel toward each other. One train travels at 95 miles per hour while the other travels at 115 miles per hourHow long will it take for the two trains to meet?
Hola👋🏻 Toca en "Crear Nueva Tarea" para enviar tu problema de matemáticas. ¡Uno de nuestros expertos comenzará a trabajar en ello de inmediato!
Exercise The temperature T in degrees Celsius of a chemical reaction is given as a function of time t, expressed in minutes, by the function defined on ¿ by: T (t )=(20 t +10)e−0.5t. 1) What is the initial temperature? 2) Show that T' (t )=(−10 t +15)e−0 .5t. 3) Study the sign of T' (t ), then draw up the table of variations of T . We do not ask for the limit of T in +∞. 4) What is the maximum temperature reached by the reaction chemical. We will give an approximate value to within 10−2. 5) After how long does the temperature T go back down to its initial value? We will give an approximate value of this time in minutes and seconds. DM 2: study of a function Exercise The temperature T in degrees Celsius of a chemical reaction is given as a function of time t, expressed in minutes, by the function defined on ¿ by: T (t )=(20 t +10)e−0.5t. 1) What is the initial temperature? 2) Show that T' (t )=(−10 t +15)e−0.5 t. 3) Study the sign of T' (t ), then draw up the table of variations of T . We do not ask for the limit of T in +∞. 4) What is the maximum temperature reached by the reaction chemical. We will give an approximate value to within 10−2. 5) After how long does the temperature T go back down to its initial value? We will give an approximate value of this time in minutes and seconds.
Question 3 A square has a perimeter given by the algebraic expression 24x – 16. Write the algebraic expression that represents one of its sides.

You might be interested in