Question

The sides of a triangle are 5, 12 and 13 units respectively. a rectangle is constructed which is equal in area to the triangle and has width of 10 units. then the perimeter of the rectangle is

Answer 1

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Answer 2

Given:

$\text{Sides of the triangle are 5 units, 12 units and 13 units.}$

$\text{A rectangle has a width of 10 units}$

$\text{The area of the triangle is equal to the area of a rectangle}$.

To Find:

$\text{Perimeter of the rectangle.}$

Formula:

$\text{Area of a triangle} = \sqrt{s(s - a)(s - b) (s - c)}$

$\text{Area of a rectangle} = \text{Length} \times \text{Breadth}$

$\text{Perimeter of a rectangle} = 2(\text{Length} +\text{Breadth})$

Find the area of the triangle:

$\text{Area of a triangle} = \sqrt{s(s - a)(s - b) (s - c)}$

$s = \dfrac{1}{2}(5 + 12 + 13)$

$s = 15$

$\text{Area of the triangle} = \sqrt{15(15 - 5)(15 - 12) (15 - 13)}$

$\text{Area of the triangle} = \sqrt{900}$

$\text{Area of the triangle} = 30 \text{ units}^2$

Find the length of the rectangle:

$\text{Area of a rectangle} = \text{Length} \times \text{Breadth}$

$30 = \text{Length} \times 10$

$\text{Length} = 30 \div 10$

$\text{Length} = 3 \text{ units}$

Find the perimeter of the rectangle:

$\text{Perimeter of a rectangle} = 2(\text{3} +\text{10})$

$\text{Perimeter of a rectangle} = 26 \text{ units}$

$\boxed {\textbf{Answer: The perimeter of the rectangle is 26 units}}$