Question

In a right triangle, one of the legs is 5 cm smaller than the hypotenuse, and the other leg is 10 cm smaller than the hypotenuse. Find the length of the hypotenuse.

Answer 1

Answer:

25 cm

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Answer 2

❥${\underline{\underline{\huge{\mathtt{ANSWER:-}}}}}$

Length of Hypotenuse is 25 cm.

❥${\underline{\underline{\huge{\mathtt{EXPLANATION:-}}}}}$

•Given:-

In a right triangle, one of the legs is 5 cm smaller than the hypotenuse, and the other leg is 10 cm smaller than the hypotenuse.

•To find:-

The length of the hypotenuse.

•Solution:-

According to the attachment,

Let the hypotenuse be AC.

Two others legs are AB and BC.

So, According to the question,

AB = AC - 5............(i)

BC = AC -10...........(ii)

We know,

${\sf{\boxed{Height^2+Base^2=Hypotenuse^2}}}$

AB² + BC² = AC²

→(AC-5)²+(AC-10)² = AC²

→AC²-10AC+25+AC²-20AC+100=AC²

→AC²-30AC+125=0

→(AC-25)(AC-5) = 0

AC-25=0

→AC = 25

Hypotenuse = 25 cm.