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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