Question : The base of a triangle is equal to the perimeter of a square whose diagonal is $9 \sqrt{2}$ cm and its height is equal to the side of a square whose area is 144 cm2. The area of the triangle(in cm2) is:
Option 1: 216
Option 2: 72
Option 3: 144
Option 4: 288
Correct Answer: 216
Solution : Diagonal of square = $9 \sqrt{2}$ cm Now, $\sqrt 2$ × side of square = $9 \sqrt{2}$ ⇒ Side of square = 9 cm So, the perimeter of square = 4 × 9 = 36 cm Base of triangle, $b$ = 36 cm Area of square = 144 cm 2 Also, the side of square = $\sqrt{144}$ = 12 cm Height of the triangle, $h$ = 12 cm Now, the area of triangle = $\frac{1}{2}×b×h$ = $\frac{1}{2} × 12 × 36$ = 216 cm 2 Hence, the correct answer is 216.
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