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  1. If a and b are the lengths of the sides of a right triangle whose hypotenuse is 10 and whose area is 20, then the value of (a + b)² is
    1. 140
    2. 180
    3. 120
    4. 160
Correct Option: B

Using Rule 1,

BC = a units, AB = b units
AC = √a² + b² = 10
⇒ a² + b² = 100 .......(i)
Area of ∆ABC

=
1
× base × height
2

=
1
ab
2

1
ab = 20
2

⇒ ab = 40 square units........(ii)
7there4; (a + b)² = a² + b² + 2ab
= 100 + 2 × 40 = 180 square units



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