The area of a rectangle is $96 c m^{2}$ and its length is $12 c m$ . The perimeter of the rectangle is same as the perimeter of a triangle. Find the semi perimeter of the triangle.

10 cm

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40 cm

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20 cm

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80 cm

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Solution

The correct option is C
20 cm

Area of a rectangle = length $\times$ breadth

$\Rightarrow$ 96 = 12 $\times$ breadth

Breadth = 8 cm

Perimeter of the rectangle = 2(length + breadth) = 2(12+8) cm = 40 cm

Perimeter of the rectangle = Perimeter of the triangle

Therefore, semi perimeter of the triangle $= \frac{40}{2} = 20 c m$

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The area of a rectangle is 96 cm2 and its length is 12 cm. The perimeter of the rectangle is same as the perimeter of a triangle. Find the semi perimeter of the triangle.

The correct option is C 20 cm Area of a rectangle = length × breadth ⇒ 96 = 12 × breadth Breadth = 8 cm Perimeter of the rectangle = 2(length + breadth) = 2(12+8) cm = 40 cm Perimeter of the rectangle = Perimeter of the triangle Therefore, semi perimeter of the triangle =402=20 cm

The area of a rectangle is $96 c m^{2}$ and its length is $12 c m$ . The perimeter of the rectangle is same as the perimeter of a triangle. Find the semi perimeter of the triangle.