Question

the perimetere pf right angle triangle is 60 cm. its hypotenuse is 26cm. find other two side and area.

Answer 1

In the Right Angle ∆ABC

Hypotenuse(c)= 26cm

Suppose, other sides are a and b.

Now, the perimeter of the ∆ABC= 60 cm

=> a + b + c = 60cm

=> a + b + 26 = 60

=> a + b = 60 - 26

=> a + b = 34 ..................equation 1.

Now, By the Pythagoras Theorem:-

c^2 = a^2 + b^2

(26)^2 = a^2 + (34 - a)^2 .....by equation 1.

676 = a^2 + 1156 + a^2 - 68a

2(a)^2 - 68a + 1156 - 676 =0

2(a)^2 - 68a + 480 = 0

a^2 - 34a + 240 = 0 ..... on dividing both sides by 2

a^2 - (24 + 10)a + 240 = 0

a^2- 24a - 10a + 240 = 0

a(a-24) - 10(a-24) = 0

(a - 10)(a - 24) = 0

So, If (a - 10) = 0 And, If (a - 24) = 0

a = 10 a = 24

So, If a = 10cm,, then b = 34 - 10 = 24cm

And,If a = 24cm,, then b = 34 -24 = 10 cm.


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