Question 32

The side of a square is equal to height of a triangle. If the area of the triangle is 294 m² and the respective ratio of its height and base is 3 : 4, what is the perimeter of the square (in m) ?

Solution

Let height of triangle = $$3x$$

=> Base of triangle = $$4x$$

=> Area of triangle = $$\frac{1}{2} \times 3x \times 4x = 294$$

=> $$6x^2 = 294$$

=> $$x^2 = \frac{294}{6} = 49$$

=> $$x = \sqrt{49} = 7$$

=> Height of triangle = $$3 \times 7 = 21$$ m

Also, side of square = height of triangle = 21 m

$$\therefore$$ Perimeter of square = $$4 \times 21$$

= $$84$$ m

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