Question

The area of a triangle metal plate with base 88 cm and altitude 64 cm is to be reduced to one-fourth of its original area by making a hole of circular shape at the center. The radius of this hole will be:

Accepted Answer

D. Original area of triangular plate = $\frac{1}{2} 	imes 88 	imes 64 = 2816	ext{ cm}^2$. Area reduced = $\frac{3}{4} 	imes 2816 = 2112	ext{ cm}^2$, which equals the area of the circular hole. $$\pi r^2 = 2112$$ $$\frac{22}{7} r^2 = 2112 \implies r^2 = \frac{2112 	imes 7}{22} = 672$$ $$r = \sqrt{672} = \sqrt{16 	imes 42} = 4\sqrt{42}	ext{ cm.}$$

Radius of circular hole in triangle

Explanation

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