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Let a and b denote llie lengths of the l...

Let a and b denote llie lengths of the legs of a right triangle with following properties:
(i) All three sides of the triangle are integers.
(ii) The perimeter of the triangle is numerically equal to its area.
(iii) a ltb.
Statement-1: The number of such triangle is 2
Statement-2: Maximum possible perimeter of the triangle is 30°.

A

Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement- 2 is True.

Text Solution

Verified by Experts

Let c be the length of the hypotenuse of the triangle. Then, a, b, c are Pythagorean triplets.
Clearly, (6, 8, 10) and (5, 12, 13) are two triplets satisfying.
`a+b+c=1/2ab`
Hence, statement-1 and 2 both are true.
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