Question

The perimeters of two similar triangles are 30 cm and 24 cm. If one side of first triangle is 12 cm, determine the corresponding side of the second triangle.

• A. 8.2 cm
• B. 9 cm
• C. 9.6 cm
• D. 10 cm

Answer 1

The correct option is C

9.6 cm

Let we are given $\Delta ABC$ and $\Delta PQR$ are similar.

Perimeter of $\Delta ABC$ =30 cm and perimeter of $\Delta PQR$ =24 cm and side BC =12 cm.

Now we have to find the length of QR, the corresponding side of $\Delta PQR$

Since $\Delta ABC\sim \Delta PQR$, we have,

$\frac{AB}{PQ}=\frac{BC}{QR}=\frac{CA}{RP}=\frac{AB+BC+CA}{PQ+QR+RP}=\frac{30}{24}$

Now $\frac{BC}{QR}=\frac{30}{24}\Rightarrow \frac{12}{QR}=\frac{30}{24}$

$\therefore QR=\frac{12\times 24}{30}=\frac{48}{5}=9.6cm.$