Question

The sum of the sides of a right angled triangle containing right angle is 17cm.If its area is 30 sq. cm. Find the length of the hypotenuse of the triangle.​

Answer 1

Answer:

The area of a right triangle = 1/2 × b × h = 30 cm²

Or, b × h = 30×2

Or, b×h = 60

BY Pythagoras Theorem,

b²+h² = 13²

Or, b²+h² = 169

By Formula

(b+h)²=b²+h²+2bh

Or, (b+h)²=169+2×60

Or, (b+h)²=169+120

Or, (b+h)²=289

Or, (b+h)²=17²

Or, b+h=17 ---------- (1)

By Formula

(b-h)²=(b+h)²-4bh

Or, (b-h)²=(17)²-4×60

Or, (b-h)²=289–240

Or, (b-h)²=49

Or, (b-h)²=7²

Or, b-h=7 ---------- (2)

Adding eq. (1) and (2)

b+h+b-h = 17+7

Or, 2b = 24

Or, b = 24/2

Or, b = 12 cm

Putting b = 12 in eq. (2)

12-h = 7

Or, h = 12 - 7

Or, h = 5 cm

The difference between other two sides = b - h

Or, The difference between other two sides = 12 - 5

Or, The difference between other two sides = 7 cm

Therefore, the difference between other two sides = 7 cm