Question

The area of a right-angled triangle is 40 cm. If one of its legs measure 8 cm, find the length of other
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Answer 1

Step-by-step explanation:

Let the hypotenuse AC=h and the other two sides be AB=a and BC=b

By Pythagoras theorem, we have h

2

=a

2

+b

2

.....(1)

Given:Area of △ABC=40sq.m

Hence,

2

1

×a×b=40

⇒ab=80 .......(2)

Given perimeter of △ABC=40 cm

That is a+b+h=40

⇒a+b=40–h

Squaring on both the sides, we get

(a+b)

2

=(40−h)

2

⇒a

2

+b

2

+2ab=1600−80h+h

2

⇒h

2

+2(80)=1600−80h+h

2

from (1) and (2)

⇒160=1600−80h

⇒80h=1600–160=1440

∴h=18 cm

Thus the length of hypotenuse is 18 cm.