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.

Name: Solved: 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. - MathMaster
Brand: MathMaster
Rating: 4.9 (162 reviews)

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

117 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)

Math Question: Calculate the limit as x approaches infinity of (3x^2 + 2x + 1) / (x^2 + 5x - 1).

Math question: What is the probability of rolling a sum of 7 with two fair six-sided dice?

What is the probability of observing exactly 3 successful outcomes in 5 independent trials, with a success rate of 0.4?

New questions in Mathematics

Simplify the expression sin³(x)+cos³(x), using trigonometric functions

-6(3x-4)=-6

Determine the absolute extrema of the function 𝑓(𝑥)=𝑥3−18𝑥2 96𝑥 , on the interval [1,10]

Suppose X has a Poisson distribution, with a mean of 0.4. Determine the probability that x is at most 2.

-3x 2y = -6; -5x 10y = 30

Pedro had 80% of the amount needed to buy a game. Of this amount, you spent 15% on a watch and therefore, you will need to add another R$640.00 to purchase this game. Is the value of the game?

Find 2 numbers whose sum is 47 and whose subtraction is 13

3.24 ÷ 82

30y - y . y = 144

Fill in the P(X-x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are -5 ,3 , 4, 5 , and 6.

List five numbers that belong to the 5 (mod 6) numbers. Alternate phrasing, list five numbers that satisfy equation x = 5 (mod 6)

Take the limit of (sin(x-4))/(tan(x^2 - 16) as x approaches 4.

(X+2)(x+3)=4x+18

there are 500,000 bacteria at the end of a pin point. 1000 bacteria can make a person sick. then bacteria at the tip of a pin point can make 500 people sick. Also, many people do not know that bacteria can (reproduce). Let's say there are 5 bacteria and we leave it for 15 minutes. bacteria will multiply to 10. if left for up to 30 minutes, 20 bacteria will form. if left up to 45 minutes. bacteria will multiply up to 40. every 15 minutes the bacteria will double 2. if you start with five bacteria that reproduce every 15 minutes, how manu bacteria would you have after 12 hours ?

22. Let [AB] be a chord in a circle C, and k a circle which is internally tangent to the circle C at a point P and to the chord [AB] at a point Q. Show that the line P Q passes through the midpoint of the arc AB opposite to the arc APB.

a coffee shop has 9 types of creamer and 11 types of sweetener. In how any ways can a person make their coffee?

Emile organizes a community dance to raise funds. In addition to paying $300 to rent the room, she must rent chairs at $2 each. The quantity of chairs rented will be equal to the number of tickets sold. She sells tickets for $7 each. How much should she sell to raise money?

answer this math question The scale on a map is drawn so that 5.5 inches corresponds to an actual distance of 225 miles. If two cities are 12.75 inches apart on the map, how many miles apart are they? (Round to the nearest tenth) miles apart. The two cities are how many miles apart

The company produces a product with a variable cost of $90 per unit. With fixed costs of $150,000 and a selling price of $1,200 per item, how many units must be sold to achieve a profit of $400,000?

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?

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.

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.

You might be interested in