Question

Given the diagram below, find the value of x. Then find AC,

Answer 1

Answer:

$x=5,\\AC=14$

Step-by-step explanation:

Since one triangle is inscribed in another, the two triangles are similar. As marked in the diagram, the sides of the larger triangle are exactly two times larger than the corresponding sides of the smaller triangle.

Therefore, we have:

$2(x+2)=4x-6,\\2x+4=4x-6,\\10=2x,\\x=\boxed{5}$

Since AC is marked by $4x-6$:

$AC=4(5)-6,\\AC=20-6,\\AC=\boxed{14}$