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(D) From the figure,the rectangle has dimensions $12 	imes 9$. The area of the rectangle is $12 	imes 9 = 108 	ext{ sq units}$.The triangular corne

Vedclass · Accepted Answer

$\frac{17}{18}$

Vedclass · Answer

(D) From the figure,the rectangle has dimensions $12 	imes 9$. The area of the rectangle is $12 	imes 9 = 108 	ext{ sq units}$.The triangular corner cut from the rectangle has legs of length $3$ and $4$,and a hypotenuse of length $5$.The area of this right-angled triangle is $\frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes 4 	imes 3 = 6 	ext{ sq units}$.The area of the resulting pentagon is the area of the rectangle minus the area of the triangle: $108 - 6 = 102 	ext{ sq units}$.The ratio of the area of the pentagon to the area of the rectangle is $\frac{102}{108}$.Dividing both numerator and denominator by $6$,we get $\frac{17}{18}$.

$A$ triangular corner is cut from a rectangular piece of paper and the resulting pentagon has sides $5, 6, 8, 9, 12$ in some order. The ratio of the area of the pentagon to the area of the rectangle is

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