Question

What is the value of x? Enter your answer in the box. x

Answer 1

Answer:

x = 9

Step-by-step explanation:

In a pair of similar triangles, corresponding sides are proportional.

Therefore,

$\dfrac{9}{9+72}=\dfrac{3x-20}{3x-20+56}$

$\implies \dfrac{9}{81}=\dfrac{3x-20}{3x+36}$

$\implies \dfrac19=\dfrac{3x-20}{3x+36}$

Cross multiply:

$\implies 3x+36=9(3x-20)$

Expand brackets:

$\implies 3x+36=27x-180$

Gather and combine like terms:

$\implies -24x=-216$

Divide both sides by -24:

$\implies x=9$

Answer 2

Apply Thales theorem

$\\ \tt\hookrightarrow \dfrac{9}{72}=\dfrac{3x-20}{56}$

$\\ \tt\hookrightarrow \dfrac{1}{8}=\dfrac{3x-20}{56}$

$\\ \tt\hookrightarrow 3x-20=56/8$

$\\ \tt\hookrightarrow 3x-20=7$

$\\ \tt\hookrightarrow 3x=27$

$\\ \tt\hookrightarrow x=9$