Question

The areas of two similar triangles are 144 cm² and 196 cm² respectively. If the longest side of the smaller triangle is 24 cm, then find the longest side of the larger triangle.

• A. 24 cm
• B. 28 cm
• C. 22 cm
• D. 26 cm

Answer 1

Answer:

B. 28 cm

Solution:

Given:

The areas of two similar triangles are 144 cm2 and 196 cm2 respectively.

If the longest side of the smaller triangle is 24 cm

Concept Used:

If Two triangle are similar,

Area of two triangle ratio = Square of the longest side ratio 

Area of Smaller triangle/Area of Larger triangle = Square of longest side smaller triangle/Square of longest side of larger triangle

Calculation:

According to the question,

Let the longest side of larger triangle be y

Area of Smaller triangle/Area of Larger triangle = Square of longest side smaller triangle/Square of longest side of larger triangle

⇒ 144/196 = (24/y)²

⇒ 24/y = 12/14

⇒ y = 28 cm

∴ The longest side of the larger triangle is 28 cm.