Question

$\Delta$DEF and $\Delta$PQR are similar triangles. If the perimeter of $\Delta$DEF is 28 cm and ratio of corresponding sides of $\Delta$DEF and $\Delta$PQR is 2 : 1, find the perimeter of the $\Delta$PQR.

• A. 56 cm
• B. 28 cm
• C. 14 cm
• D. 10 cm

Answer 1

The correct option is C 14 cm

Given: $\Delta$DEF $\sim$ $\Delta$PQR, ratio of corresponding sides = 2 : 1

So, $\frac{DE}{PQ}=\frac{EF}{QR}=\frac{DF}{PR}=\frac{2}{1}$

DE = 2PQ, EF = 2QR, and DF = 2PR

Perimeter of $\Delta$DEF = DE + EF + DF
28 = 2PQ + 2QR + 2PR
28 = 2(PQ + QR + PR)
28 = 2(Perimeter of $\Delta$PQR)
​​​​​​​Perimeter of $\Delta$PQR = 14 cm