Question

The perimeter of an isosceles triangle is 32cm. The base is 2cm more than the equal side. Find the area of the triangle.​

Answer 1

Solution

SolutionGiven :-

• Perimeter of issosceles triangle = 32 cm
• The base is 2cm more than the equal side

Find :-

• Area of issosceles triangle

Explanation

Let,

• Equal side of triangle = a

According to question,

==> Base (b ) = 2 + a

So, Perimeter of issosceles triangle

==> (2a + b) = 32

==> 2a + (2 + a) = 32

==> 3a = 32 - 2

==> 3a = 30

==> a = 30/3

==> a = 30/3

==> a = 10 cm

Since,

• Base be of issosceles triangle = (2 + a) = 2 + 10 = 12 cm

Now, Calculate area

==> Area of issosceles triangle = 1/2 × b × √[ a² - b²/4]

==> Area of issosceles triangle = 1/2 × 12 × √[ 10² - 12²/4]

==> Area of issosceles triangle = 6 × √[ 100 - 144/4]

==> Area of issosceles triangle = 6 × √[ 100 - 36]

==> Area of issosceles triangle = 6 × √[64]

==> Area of issosceles triangle = 6 × 8

==> Area of issosceles triangle = 48 cm²

Hence

• Area of issosceles triangle will be = 48 cm²

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