Question

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

Answer 1

The value of x is 8.

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

`(PQ)/(QR)=(XZ)/(ZY)`

`(21)/(28)=(5x+2)/(7x)`

`(3)/(4)=(5x+2)/(7x)`

`7x* 3=(5x+2)* 4`

`21x=20x+8`

`21x-20x=8`

`x=8`

Therefore the value of x is 8.