Question

The ratio of areas of two similar triangles is $2\frac{1}{4}:1$. If the perimeter of large triangle is 36 cm, then find the perimeter of smaller triangle.

• A. 16 cm
• B. 20 cm
• C. 12 cm
• D. 24 cm

Answer 1

The correct option is A 16 cm

Ratio of areas of two similar triangles is $\frac{9}{4}:1=2.25:1$.

$2.25x$ is the area of larger triangle

Perimeter of large triangle is $36$ cm

Area of triangle $=\frac{1}{2}$ perimeter of triangle

$\therefore 2.25x=\frac{36}{2}cm$

$⟹x=8$

Thus, area of smaller triangle is $8$ cm.

$\therefore$ Perimeter of smaller triangle $=2\times 8=16$ cm