Question

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

Answer 1

Apply Thales theorem

`\\ \tt\hookrightarrow (9)/(72)=(3x-20)/(56)`

`\\ \tt\hookrightarrow (1)/(8)=(3x-20)/(56)`

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

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

`\\ \tt\hookrightarrow 3x=27`

`\\ \tt\hookrightarrow x=9`

Answer 2

x = 9

Explanation:

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

Therefore,

`(9)/(9+72)=(3x-20)/(3x-20+56)`

`\implies (9)/(81)=(3x-20)/(3x+36)`

`\implies \frac19=(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`