Question

Ratio of areas of two triangles with equal heights is 3 : 4. If base of smaller triangle is 6 cm, what is the corresponding base of bigger triangle?

Answer 1

Given,

The ratio of the area of the two triangles = 3:4

Base of the smaller triangle = 6 cm

To find,

The base of the bigger triangle.

Solution,

Let, the area of the two triangles = 3x cm² and 4x cm²

(Assume x as a variable to do the further mathematical calculations.)

Area of the smaller triangle = 3x cm²

Let, the height of the both triangles = h cm

Area of smaller triangle = ½ × 6 × h = 3h cm

3h = 3x

h = x

Now, let the base of the bigger triangle = b cm

½ × h × b = 4x

½ × x × b = 4x

b = 4x × 1/x × 2

b = 8

Hence, the base of the bigger triangle is 8 cm.