Question

A triangle is cut by a line s parallel to the base in such a way that it divides the side of the triangle into parts in the ratio of 2 : 3. Find the other side of the triangle if it is known that the line s divides it into parts whose length is 5 cm.

162

likes
811 views

Answer to a math question A triangle is cut by a line s parallel to the base in such a way that it divides the side of the triangle into parts in the ratio of 2 : 3. Find the other side of the triangle if it is known that the line s divides it into parts whose length is 5 cm.

Expert avatar
Hester
4.8
116 Answers
Let's denote the sides of the triangle as follows: Let AB be the base of the triangle, and CD be the line parallel to the base AB that divides the side into parts in the ratio of 2:3. Let \( E \) be the point of intersection between CD and \( AB \). So, \( AE \) represents 2 parts and \( EB \) represents 3 parts. Given that the length of the line \( CD \) is 5 cm, we can express \( AE \) and \( EB \) in terms of this information. Let \( x \) be the length of \( AE \), then \( 5 - x \) will be the length of \( EB \). Since the parts are in the ratio 2:3, we can set up the following proportion: \[ \frac{x}{5-x} = \frac{2}{3} \] Now, cross-multiply to solve for \( x \): \[ 3x = 2(5 - x) \] \[ 3x = 10 - 2x \] \[ 5x = 10 \] \[ x = 2 \] So, the length of \( AE \) is 2 cm, and the length of \( EB \) is \( 5 - 2 = 3 \) cm. Now, you know the lengths of \( AE \) and \( EB \). If \( AC \) is the other side of the triangle, then \( AC = AE + EC \). Substitute the values: \[ AC = 2 + 3 = 5 \] Therefore, the length of the other side of the triangle, AC, is 5 cm.

Frequently asked questions (FAQs)
What is the equation for a hyperbola with a horizontal transverse axis, center at (h,k), and vertices (h±a,k)?
+
What is the value of square root function when the input is 25?
+
What is the measure of angle A in a triangle if angle B measures 60° and angle C measures 45°?
+
New questions in Mathematics
If we have the sequence: 3, 6, 12, 24 Please determine the 14th term.
given cos26=k find cos13
Suppose that a device has been created that launches objects at ground level and that its operation is modeled by the function h(x) = -4ײ + 256x, with h being the height (in meters) and x being the distance (in meters) What is the maximum height that the object reaches?
x/20*100
The mean temperature for july in H-town 73 degrees fahrenheit. Assuming that the distribution of temperature is normal what would the standart deviation have to be if 5% of the days in july have a temperature of at least 87 degrees?
Determine the absolute extrema of the function 𝑓(𝑥)=𝑥3−18𝑥2 96𝑥 , on the interval [1,10]
30. In 8 s, a car that starts from rest and moves with uniformly accelerated motion has achieved a speed of 72m/s. How much space must it travel to reach a speed of 90m/s? Sunshine: 450 m
Suppose 56% of politicians are lawyers if a random sample of size 873 is selected, what is the probability that the proportion of politicians who are lawyers will be less than 55% round your answer to four decimal places
3.24 ÷ 82
There are 3 orchards, a, b and c. Orchard a has 60 fewer trees than orchard b orchard c has 3 times as many trees as orchard b. If the three orchards have 430 trees altogether, how many trees does orchard c have?
Use linear approximation to estimate the value of the sine of 31o.
A function is considered exponential when it has a base with positive values greater than zero and different from one, where the exponent is an unknown. An important characteristic of exponential functions is that they show rapid growth or decay as an independent variable increases or decreases. Given the function 25^(x+3)=125, it is calculated that x has the value of
(X+2)(x+3)=4x+18
17. A loan for $104259 is taken out for 10 years with an annual interest rate of 9.4%, compounded quarterly. What quarterly payment is required to pay the loan off in 10 years? Enter to the nearest cent (two decimals). Do not use $ signs or commas in the answer.
factor the polynomial completely over the set of complex numbers b(x)=x^4-2x^3-17x^2+4x+30
solve R the following equation 4 x squared - 35 - 9 over x squared is equal to 0
calculate the product of 4 and 1/8
The perimeter of a rectangular rug is 42 feet. The width is 9 feet. What is the length?
5 1/9 + 2 2/3
An invoice for €2,880 plus default interest of €48.40 was paid on October 28th. Interest rate 5.5%. When was the bill due?