Direction: In each of the following questions, a question is asked followed by three statements. You have to study the questions and all the three statements given and decide whether any information provided in the statement(s) is/are redundant and can be dispensed with while answering the questions.
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What is the area of a right-angled triangle?
A. The perimeter of the triangle is 30 cm.
B. The ratio between the base and the height of the triangle is 5 : 12.
C. The area of the triangle is equal to the area of rectangle of length 10 cm.
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- Only B and C together are required
- Only A and B together are required
- Only either A or B and C together are required
- Only A and C together are required
- None of these
Correct Option: B
Let, the base, height and hypotenuse of a right-angled triangle be b, p and h, respectively.
From Statement A, b + P + h = 30 …(1)
From Statement B, b : p = 5 : 12 …(2)
Let the base of triangle is 5k and height of triangle is 12k .
We know that
h2 = p2 + b2 = 25k2 + 144k2 = 169k2
∴ h = 13k …(3)
Combining equations (1), (2) and (3), we get
5k + 12k + 13k = 30 ⇒ k = 1
| ∴ Area of triangle = | 1 | x 5 x 12 = 30 cm2 |
| 2 |
Hence, only A and B together are sufficient.
