Question

A triangle has its longest side 20 cm and another of its sides has length 10cm.Its area is 80 cm2. What is the exact length of its third side?

Answer 1

Given - Longest side of triangle - 20 cm

Another side length - 10 cm

Area of triangle - 80 cm²

Find - Length of third side.

Solution - Let A,B and C be three sides of triangle. AB is the base of triangle 20 cm and h be the height of triangle, CD. BD is side of triangle 10 cm and AD be unknown side.

As per the formula of area of triangle Area = b*h/2.

Keeping the values in formula -

80 = 20*h/2

h = 160/20

h = 8 cm.

Finding out the length of CB.

Length of CB² = BD² - CD²

CB² = 10² - 8²

CB² = 100 - 64

CB = ✓36 = 6 cm.

Now, finding third side of triangle, AD.

AC = AB - CB = 20 - 6 = 14 cm

AD² = AC² + CD²

AD² = 14² + 8²

AD² = 196 + 64

AD = 16.12 cm.

Thus, length of third side of triangle is 16.12 cm.