Question

In a right angle triangle,the hypotenuse is 10cm more than the shortest side. If the third side is 6cm less than hypotenuse,find the sides of the triangle​

Answer 1

Let the RAT have its hypotenuse as H, and the other two sides as L and S,

H = 6+2S …(1)

L = H-2 or L = 6+2S-2 = 4+2S …(2)

H^2 = L^2+S^2, or

(6+2S)^2 = (4+2S)^2+S^2, or

36+24S+4S^2 = 16+16S+4S^2+S^2, or

S^2–8S-20=0 or,

S = [8+(64+80)^0.5]/2

= [8+12]/2 = 10

H = 6+2*10 = 26

L = 4+2S = 24

Check: H^2 = 26^2 = 676

L^2+S^2 = 24^2 + 10^2 = 576 + 100 = 676 = H^2. Correct.

The three sides of the triangle are 10, 24 and 26 units.