Question

Find the area of a triangle having perimeter 32cm one side 11cm and difference of other two sides is 5cm

Answer 1

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Answer 2

Solutions :-

We have,

Perimeter of triangle = 32 cm
One of its side = 11 cm

Let the second side be x
And third side be x + 5

Perimeter of triangle = sum of three sides

A/q

=> 11 + x + x + 5 = 32
=> 2x = 32 - 16
=> 2x = 16
=> x = 16/2 = 8

So, second side = x = 8 cm
Third side = x + 5 = 8 + 5 = 13 cm

$Semi \: perimeter = \frac{a + b + c}{2} \\ \\ = \frac{11 + 8 + 13}{2} = \frac{32}{2} = 16 \: cm$

Now,

By using heron's formula,

Find the area of a triangle :-

$area \: = \sqrt{s(s - a)(s - b)(s - c) } \\ \\ = \sqrt{16(16 - 11)(16 - 8)(16 - 13) } \\ \\ = \sqrt{16 \times 5 \times 8 \times 3} \\ \\ = \sqrt{1920} = 43.81 \: approx.$

Answer : Area of triangle = 43.81 cm²