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The sides of a triangle are $5$ , $12$ and $13$ units. A rectangle of width $10$ units are constructed equal in area to the area of the triangle. Then what is the perimeter of the rectangle?

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30 units

26 units

13 units

15 units

answer is B.

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Detailed Solution

Given, the sides of a triangle are

5

12

and

13

units.
A rectangle of width

10

units are constructed equal in area to the area of the triangle.
Consider

5^{2} + 1 2^{2} = 25 + 144

\Rightarrow

5^{2} + 1 2^{2} = 169

\Rightarrow

5^{2} + 1 2^{2} = 1 3^{2}

This equation proves the pythagorean theorem. So, the given triangle is a right angled triangle.
Area of a triangle is

\frac{1}{2}

(Base)(Height).

\Rightarrow

Area of the triangle

= \frac{1}{2} \times 12 \times 5 sq . units .

\Rightarrow

Area of the triangle

= 30

sq. units
Area of a rectangle is length×breadth.
Area of the rectangle = Area of the triangle..

\Rightarrow

length \times breadth = 30

\Rightarrow Length = \frac{30}{breadth}

\Rightarrow

Length

= \frac{30}{10}

\Rightarrow

Length

= 3 units

Perimeter of a rectangle = 2(length + breadth).

\Rightarrow

Perimeter of the rectangle

= 2 \times (10 + 3)

units

\Rightarrow

Perimeter of the rectangle

= 26

units.
Hence, option 2 is correct.

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