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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Which is the area of the given right-angled triangle?
A. Length of the diagonal of rectangle is 5 cm.
B. Perimeter of the triangle is four times its base.
C. One of the angles of the triangle is of 60°.
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- C only
- A and C only
- B or C only
- B and C both
- A or B or C
Correct Option: B
Let, the length and breadth of the rectangle be l and b, respectively.
From statement A → Diagonal of rectangle ( h ) = 5 ⇒ l2 + b2 = 25
From statement B → l + b + h = 4b ⇒ l = 3b − 5
From statement C → One of the angles of the triangle = 60°
From statement A and B , ( 3b - 5 )2 + b2 = 25 ⇒ 9b2 + 25 - 30b + b2 = 25
⇒ 9b2 - 30b + b2 = 0 ⇒ 10b2 - 30b = 0 ⇒ 10b( b - 3 ) = 0 ⇒ b = 3 cm
∴ l = 3 x 3 - 5 = 9 - 5 = 4 cm
∴ Area of right angle triangle = ( 1 / 2 ) x base x height
= ( 1 / 2 ) x 3 x 4 = 6 cm2
After combining any of the above two statements, we get the values of l and b. Hence, any of them can be dispensed with.
