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The base of an isosceles triangle is 6 cm and each of its equal sides is 5 cm. The height of the triangle is ____ cm.

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Detailed Solution

The base of an isosceles triangle is 6 cm and each of its equal sides is 5 cm. The height of the triangle is 4 cm.
Given the base of an isosceles triangle is 6 cm and each of its equal sides is 5 cm.
The value of semi-perimeter (s) is,

s = a + b + c 2 ⇒ s = 5 + 6 + 5 2 cm ⇒ s = 162 c m ⇒ s = 8 c m

Using Heron’s formula to calculate area,

A = s (s − a) (s − b) (s − c) ⇒ A = 8 8 − 5 × 8 − 6 × 8 − 5 cm 2 ⇒ A = 8 × 3 × 2 × 3 cm 2 ⇒ A = 144 cm 2 ⇒ A = 12 cm 2

Also, area of triangle is,

A r e a = 12 × b a s e × h e i g h t ⇒ 12 = 12 × 6 × H e i g h t ⇒ 12 = 62 × H e i g h t ⇒ H e i g h t = 12 × 2 6 ⇒ H e i g h t = 4 c m

The height of triangle is 4 cm.

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