Question

the area of right angled triangle is 24 cm^2 and its hypotenuse is 10cm .Find the length of its other two sides.

Answer 1

There must be a little correction in the question-

A right triangle has a perimeter of 24 cm and a hypotenuse of 10 cm. Find the length of its other two sides.

Because if the area is given the the sides can also be in roots.

Hence,

a + b + 10 = 24

⇒ a + b = 14 ...(1)

Also, a + b = (10)

⇒ a + b = 100 ...(2)

We know that

(a + b) = a + b + 2ab

⇒ (14) = 100 + lab

⇒ 2ab = 96

⇒ ab = 48 ...(3)

Also, (a – b) = a + b – 2ab

= 100 – 2 x 48 = 100 – 9b

= 4 | if a > b

⇒ a – b = 2 ....(4)

Solving (1) and (4), we get a = 8 cm b = 6 cm

Even if the area is given then, 1/2*b*h=24

                                                 b*h= 48

By which we dont get any satisfaction for the other two sides. Hence in this case we will hv to apply hit and trial method by which 1 side=8 and other 6cm.

Thanku..