Question

A person wishes to fix three rods together in
the shape of a right-angled triangle. The
hypotenuse is 4 cm longer than the base and 8
cm longer than the altitude. Find the length
of each rod.​

Answer 1

Answer:

Let the base be x cm

Thus, perpendicular is (x−4) cm and hypotenuse is (x+8) cm

By Pythagoras theorem, we have

(Hypotenuse)

2

=(perpendicular)

2

+(base)

2

(x+4)

2

=(x−4)

2

+x

2

⇒x

2

+16+8x=x

2

+16−8x+x

2

⇒16x=x

2

⇒x=16

Then, for x=16

Hypotenuse =20 cm

Base =16 cm

Perpendicular =12 cm