Question 125

The height and base of a triangle are equal to the length and breadth of a rectangle respectively. If the perimeter of the rectangle is 86m and the difference between its length and breadth is 5m, what is the area of the triangle ? (in m^{2} )

Solution

Let length of rectangle = $$x$$ m

Breadth = $$(x - 5)$$ m

=> Perimeter of rectangle = $$2 (x + x - 5) = 86$$

=> $$2x - 5 = \frac{86}{2} = 43$$

=> $$2x = 43 + 5 = 48$$

=> $$x = \frac{48}{2} = 24$$

=> Breadth = 24 - 5 = 19 m

=> Height of triangle = 24 m and Base of triangle = 19 m

$$\therefore$$ Area of triangle = $$\frac{1}{2} \times 24 \times 19$$

= $$12 \times 19 = 228 m^2$$

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