Question

The perimeter of aright angled triangle is 30cms.the length of the hypotenuse is 13cms .find the length of the other two sides

Answer 1

Perimeter = 30 cm

Hypotenuse = 13 cm



Now,

Perimeter = Base + Height + Hypotenuse

30 = Base + Height + 13

30 - 13 = Base + Height

Base + Height = 17

Base = (17 - Height)



Now, in a right angled Triangle

(Hypotenuse)2 = (Base)2 + (Height)2

(13)2 = (17 - Height)2 + (Height)2

(13)2 = (17 - H)2 + (H)2

169 = 172 + H2 - 2(17)H + H2

169 = 2H2 - 34H + 289

0 = 2H2 - 34H + 289 - 169

2H2 - 34H + 120 = 0

2(H2 - 17H + 60) = 0

H2 - 17H + 60 = 0

H2 - 12H - 5H + 60 = 0

H(H - 12) - 5(H - 12) = 0

(H - 5) (H - 12) = 0

So, H = 5, 12



If H = 5, Base = 17 - H = 17 - 5 = 12

If H = 12, Base = 17 - H = 17 - 12 = 5



Thus, the other two sides are 12 and 5