Question

find the base of an isosceles triangle whose area is 4 root 15 square centimetre and the length of one side is equal side is 8 cm

Answer 1

Solution:

Given: Area = 4√15 and length of one side = 8

Let b be the base and h be the height.

Let the base be 2b.

Area of the triangle = 1/2 × 2b × h

4√15 = b × h

h = 4√15/b

Now, use pythagoras theorem,

b² + h² = 8²

b² + (4√15/b)² = 8²

b⁴ - 64b² + 240 =0

b⁴ - 60b² - 4b² + 240 =0

(b² - 60)(b² - 4) = 0

(b - 2√15)(b + 2√15)(b - 2)(b + 2) = 0

Negative values should be neglected.

When b is 2√15 then h is 2.

when b is 2 then h is 2√15.

Hence, the base could be 4√15 then the height will be 2 and the base could be 4 then the height will be 2√15.