Question

Find the area of a triangle with side 25,17,26cm. Also find the height of the triangle corresponding to the smallest side of the triangle

Answer 1

Given :-

Sides of the triangle are 25cm, 17cm and 26cm.

Let the sides of the triangle be a, b and c respectively.

Semi-perimeter of the triangle = (25 + 17 + 26)/2

= 68/2

= 34cm

Using heron's formula,

= √[s(s - a)(s - b)(s - c)]

= √[34(34 - 25)(34 - 17)(34 - 26)]

= √(34 × 9 × 17 × 8)

= √(2 × 17 × 3 × 3 × 17 × 2 × 2 × 2)

= √(2 × 2 × 2 × 2 × 3 × 3 × 17 × 17)

= 2 × 2 × 3 × 17

= 204cm²

The area of the triangle is 204cm²

Now, here the shortest side is 17cm.

We also know that,

1/2 × b × h = area of a triangle

➡ 1/2 × 17 × h = 204cm²

➡ h = (204 × 2)/17

➡ h = 12 × 2

➡ h = 24cm

Hence, the of the triangle corresponding to it's smallest side is 24cm.

Answer 2

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