Q25 / 60 · KVPY 2015 (SA) · Mathematics

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 rectangle is

A
$\frac{11}{18}$
B
$\frac{13}{18}$
C
$\frac{15}{18}$
Correct answer
D
$\frac{17}{18}$

Solution

Angle of Rectangle $=12 \times 9$ Area of pentagon $=12 \times 9-\frac{1}{2} \times 3 \times 4$ $=12 \times 9-6$ Required $=\frac{12 \times 9-6}{12 \times 9}=\frac{17}{18}$

Hence, the correct answer is option: 'D'.

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