Question : The base of a triangle is equal to the perimeter of a square whose diagonal is $6 \sqrt{2}$ 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: 288
Option 2: 216
Option 3: 144
Option 4: 72
Correct Answer: 144
Solution : Let $a$ be the side of the first square. Diagonal of first square = $6 \sqrt{2}$ cm $⇒a\sqrt2 = 6 \sqrt{2}$ (where $a$ is the sides of the square) $\therefore a = 6$ Perimeter $=4a= 4 × 6= 24$ cm The base of the triangle, $b$ = 24 cm Let $x$ be the side of the second square. Area of second square = 144 cm 2 $⇒x^2 = 144$ $\therefore x = \sqrt{144} = 12$ Height of the triangle, $h$ = 12 cm Area of the triangle = $\frac{1}{2}bh$ = $\frac{1}{2} × 24 × 12$ = $144$ cm 2 Hence, the correct answer is 144.
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