Question

What is x given ABC~DBE. Show your work

Answer 1

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

Solution:

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

AC = 50, DE = 30, EC = 25, BE = x, BC = 25 + x

To find the value of x:

Property of similar triangles:

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

$\frac{BE}{BC} =\frac{DE}{AC}$

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

Do cross multiplication, we get

$50x=30(25+x)$

$50x=750+30x$

Subtract 30x from both sides of the equation.

$20x=750$

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 $\frac{75}{2}$.