The area of a right-angled triangle is one-third of the area of a rectangle. The base of the triangle is 50 percent of the breadth of the rectangle. If the perimeter of the rectangle is 200 cm, what is the height of the triangle?
Solution
Correct Answer: Option D
Let the base and height of the triangle be B and H respectively.
And length and breadth of the rectangle be L and B1 respectively.
According to the given information:
The base of the triangle is 50% of the breadth of the rectangle
∴ B = ½ B1 ....... (1)
We know that, perimeter of rectangle = 2 × (length + breadth)
If the perimeter of the rectangle is 200 cm
Then, L + B1 = 100…………….. (2)
∵ Perimeter of the rectangle = 2(L + B)
Now, the area of a right-angled triangle is one-third of the area of a rectangle
∴ ½ × B × H = 1/3 × L × B1……………………. (3)
By analyzing above 3 equations and 4 unknowns
Hence, the value of H can’t be determined.
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