Q219
If a and b are the lengths of the sides of a right angled triangle whose hypotenuse is 10 and whose area is 20, then the value of ( a + b )2 is
If and are the lengths of the sides of a right angled triangle whose hypotenuse is 10 and whose area is 20, then the value of ( + )2 is
A.
140
B.
120
C.
180
AnswerD.
160
Answer: Option C
Solution
Answer: Option C
Solution:
In right ΔABC,
a2 + b2 = 102 (by pt) . . . . (i)
Area ΔABC = ab = 20
ab = 40
(a + b)2 = a2 + b2 + 2ab
= 102 + 2(40)
= 180