Question 16

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 90m and the difference between its length and breadth is 7m, what is the area of the triangle ? (in m )

Solution

Let length of rectangle = $$x$$ m

Breadth = $$(x - 7)$$ m

=> Perimeter of rectangle = $$2 (x + x - 7) = 90$$

=> $$2x - 7 = \frac{90}{2} = 45$$

=> $$2x = 45 + 7 = 52$$

=> $$x = \frac{52}{2} = 26$$

=> Breadth = 26 - 7 = 19 m

=> Height of triangle = 26 m and Base of triangle = 19 m

$$\therefore$$ Area of triangle = $$\frac{1}{2} \times 26 \times 19$$

= $$13 \times 19 = 247 m^2$$

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