Question

The triangles above are similar write a similarity statement if possible solve for x the images are not drawn to scale

Answer 1

Answer:

The value of x is 8.

Step-by-step explanation:

In triangle PQR and XZY,

$\angle P=\angle X=90^{\circ}$

$\angle Q=\angle Z$

$\angle R=\angle Y$

By AA property of similarity, we can say that

$\triangle PQR\sim \triangle XZY$

The similarity statement is $\triangle PQR\sim \triangle XZY$.

The corresponding sides of similar triangles are proportional. Since both triangles are similar, so

$\frac{PQ}{QR}=\frac{XZ}{ZY}$

$\frac{21}{28}=\frac{5x+2}{7x}$

$\frac{3}{4}=\frac{5x+2}{7x}$

$7x\times 3=(5x+2)\times 4$

$21x=20x+8$

$21x-20x=8$

$x=8$

Therefore the value of x is 8.