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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