Question

the length of the hypotenuse of a right angled triangle exceeds the length of one side by 2 cm and exceeds twice the length of other side by 1 centimetre find the length of each side also find the perimeter and the area of the triangle

Answer 1

Let hypotenuse be a

Given, base = a-2               ---------------- (1)
Given, altitude = (a-1)/2.       ---------------- (2)

By Pythagoras theorem

a^2 = (a-2) + ((a-1)/2)^2
a^2 = (a^2-2a+1)/4 + a^2-4a+4 
4a^2 = a^2-2a+1+4(a^2-4a+4)
4a^2 = a^2-2a+1+4a^2-16a+16
a^2 - 18a + 17 =0
(a-17)(a-1) = 0
a = 17

Substitute a = 17 in (2) we get

and lenght of each side = 17 - 1/2
                                         = 16/2
                                         =8.

Hope it helps you!