Question : The area of a triangle is half the area of a square. The perimeter of the square is 172 cm. What is the area of the triangle (in cm2)?
Option 1: 924.5
Option 2: 1984
Option 3: 1849
Option 4: 992
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Correct Answer: 924.5
Solution :
The perimeter of the square = 172 cm
If a is the length of the side of the square then,
4a = 172
$\therefore$ a = $\frac{172}{4}$ = 43 cm
Now, area of square = a
2
= (43)
2
Given: Area of triangle = $\frac{1}{2}$ × a
2
$\therefore$ Area of triangle = $\frac{1}{2}$ × 43
2
= 924.5 cm
2
Hence, the correct answer is 924.5.
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