Answer:
The value of x is 8.
Step-by-step explanation:
In triangle PQR and XZY,
[tex]\angle P=\angle X=90^{\circ}[/tex]
[tex]\angle Q=\angle Z[/tex]
[tex]\angle R=\angle Y[/tex]
By AA property of similarity, we can say that
[tex]\triangle PQR\sim \triangle XZY[/tex]
The similarity statement is [tex]\triangle PQR\sim \triangle XZY[/tex].
The corresponding sides of similar triangles are proportional. Since both triangles are similar, so
[tex]\frac{PQ}{QR}=\frac{XZ}{ZY}[/tex]
[tex]\frac{21}{28}=\frac{5x+2}{7x}[/tex]
[tex]\frac{3}{4}=\frac{5x+2}{7x}[/tex]
[tex]7x\times 3=(5x+2)\times 4[/tex]
[tex]21x=20x+8[/tex]
[tex]21x-20x=8[/tex]
[tex]x=8[/tex]
Therefore the value of x is 8.
