Question

If triangle HBN sim triangle LYR, find the value of x and find the length of overline RL.

A) x = 3, RL = 15
B) x = 5, RL = 25
C) x = 4, RL = 20
D) x = 6, RL = 30

Answer 1

To find the value of x and the length of RL in the given similar triangles HBN and LYR, set up a proportion between their corresponding sides. Solve for x using the proportion and calculate RL by adding RY and 3. (Option A).

Step-by-step explanation:

To find the value of x and the length of RL in the given similar triangles HBN and LYR, we can set up a proportion between their corresponding sides. Since the triangles are similar, the ratios of their corresponding sides are equal. We have:

HB/LY = BN/RY

Given that HB = 3 and BN = x, we need to find the value of x. Let's substitute the known values in the proportion:

3/LY = x/RY

Cross multiplying, we get 3 * RY = LY * x.

Since we need to find the value of x, we solve for x:

x = (3 * RY) / LY

Now, to find the length of RL, we can use the fact that HB = LY. So we have:

RL = RY + LY

Substituting the known values, we get RL = RY + 3. (Option A).