Discussion :: Area
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What is the area of a right-angled triangle?
I.
The perimeter of the triangle is 30 cm.
II.
The ratio between the base and the height of the triangle is 5 : 12.
III.
The area of the triangle is equal to the area of a rectangle of length 10 cm.
A.
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B.
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C.
I and III only |
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D.
III, and either I or II only |
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E.
None of these |
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Answer : Option A
Explanation :
From II, base : height = 5 : 12.
Let base = 5x and height = 12x.
Then, hypotenuse = \(\sqrt{(5X)^2}+{(12X})^2\)=13x
From I, perimeter of the triangle = 30 cm.
5x + 12x + 13x = 30 
x = 1.
So, base = 5x = 5 cm, height = 12x = 12 cm.
Area =[\( \frac { 1 } { 2 }\)x 5 x 12]cm2= 30 cm2.
Thus, I and II together give the answer.
Clearly III is redundant, since the breadth of the rectangle is not given.
Correct answer is (A).
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