Question

The perimeter of a right angle triangle is 30 cm. If it's hypotenuse is 13 cm, then other two sides are

Answer 1

Answer:

other 2 sides = 5 cm and 12 cm

Step-by-step explanation:

let other 2 sides = a and b

hypotenuse = h = 13

given,

a + b + h = 30

=> a + b + 13 = 30

=> a + b = 30 - 13

=> a + b = 17 ----(1)

h = 13

=> h^2 = 13^2 = 169

=> a^2 + b^2= 169

=> (a + b)^2 - 2ab = 169

=> 17^2 - 2ab = 169 (from (1))

=> 289 - 2ab = 169

=> 2ab = 289 - 169 = 120 ----(2)

=> (a - b)^2 = (a + b)^2 - 4ab

=> (a - b)^2 = 17^2 - 2×120 (from (1) & (2))

=> (a - b)^2 = 289 - 240 = 49

=> a - b = 7 ----(3)

adding (1) & (3),

2a = 24

=> a = 24/2 = 12

=> b = a - 7 = 12 - 7 = 5 (from (3))