Question

The perimeter of a right angled triangle is 60cm and its hypotenuse is 26cm. find the other two sidesthe other two sides
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Answer 1

Given perimeter of right-angled triangle is 60 cm.

hypotenuse = h = 26 cm

Let the other two sides be a & b.

So, a + b + h = 60

⇒ a + b = 60 – 26

⇒ a + b = 34 ... (i)

By Pythagoras theorem,

⇒ a2 + b2 = h2

⇒ a2 + b2 = 262

⇒ (a + b)2 – 2ab = 676

⇒ 342 – 2ab = 676

⇒ 2ab = 1156 – 676

⇒ 2ab = 480

⇒ ab = 240

Using (a – b)2 = a2 + b2 – 2ab

⇒ (a – b)2 = 676 – 2x240

⇒ (a – b)2 = 676 – 480

⇒ (a – b)2 = 196

⇒ a – b = 14 ... (ii)

adding (i) &(ii);

⇒ 2a = 48

⇒ a = 24

⇒ b = 10

So, the other two sides are 24 cm & 10cm.

Answer 2

Right angled triangle

Solve for leg

a=24cm

a=24cmor

a=24cmor10cm

c = Hypotenuse = 26 cm

cmP = Perimeter = 60 cm

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