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

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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

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Answer 1

Correct Answer: 144

Solution : Let $a$ be the side of the first square.
Diagonal of first square = $6 \sqrt{2}$ cm
$\Rightarrow a \sqrt{2} = 6 \sqrt{2}$ (where $a$ is the sides of the square)
$∴ a = 6$
Perimeter $= 4 a = 4 \times 6 = 24$ 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
$\Rightarrow x^{2} = 144$
$∴ x = \sqrt{144} = 12$
Height of the triangle, $h$ = 12 cm
Area of the triangle = $\frac{1}{2} b h$
= $\frac{1}{2} \times 24 \times 12$
= $144$ cm ²
Hence, the correct answer is 144.

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Question : The base of a triangle is equal to the perimeter of a square whose diagonal is 62 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: 288Option 2: 216Option 3: 144Option 4: 72

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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