Question

Hypotenuse of a right angled triangle is 25cm and out of the remaining two sides, one is longer than the other by 5cm. Then the length of the longer side is:

Answer 1

Answer:

20cm

Step-by-step explanation:

let consider △ABC to be a right angled △. Where AC is the hypotenuse , AB is the longer side and BC is the shorter side

Now let BC be x and AB= x+5

now on applying the Pythagorean theorem

AC^2 = AB^2 + BC^2

25^2 = (x+5)^2 + x^2

625  = x^2 + 25 + 10x + x^2

625 = 2x^2 + 10x + 25

0 = 2x^2 + 10x - 600( i.e. 25-625)

0 = x^2 + 5x - 300 (i.e. on dividing by 2)

0 = (x^2 - 15x) (20x - 300)

0= x(x - 15)  +20(x - 15)

x= 15 or  x= -20

since x cannot be negative

so, x= 15

and x+5=20

so the longer side is 20 cm