Question

What is x given triangleABC ~triangleDBE?

Answer 1

x = 37.5 (or) $\frac{75}{2}$

Solution:

Given $\triangle A B C \sim \triangle D B E$.

Let us take BE = x and BC = 25 + x.

To determine the value of x:

If two triangles are similar then the corresponding angles are congruent and the corresponding sides are in proportion.

$\frac{AC}{DE}=\frac{B C}{B E}$

$\frac{50}{30} =\frac{25+x}{x}$

Do cross multiplication, we get

$50x=30(25+x)$

$50x=750+30x$

Subtract 30x from both sides of the equation.

$20 x=750$

Divide by 20 on both sides of the equation, we get

x = 37.5 (or) $\frac{75}{2}$

Hence the value of x is 37.5 or $\frac{75}{2}$.