Question

The base of an isosceles triangle measures 80cm and its area is 360cm². Find the perimeter of the triangle.

Answer 1

Consider △ ABC as an isosceles triangle with AL perpendicular to BC

It is given that BC = 80cm and area = 360 cm²

We know that area of a triangle = ½ × b × h

By substituting the values

½ × BC × AL = 360 cm²

So we get

½ × 80 × AL = 360 cm²

On further calculation

40 × h = 360

By division

h = 9 cm

We know that BL = ½ × BC

By substituting the values

BL = ½ × 80

By division

BL = 40cm and AL = 9cm

Using the Pythagoras theorem

We know that

a = √ (BL² + AL²)

By substituting the values

a = √ (40² + 9²)

So we get

a = √ (1600 + 81)

By addition

a = √ 1681

So we get

a = 41 cm

So the perimeter of the isosceles triangle = 41 + 41 + 8

We get

Perimeter of the isosceles triangle = 162 cm

Therefore, the perimeter of the triangle is 162 cm.