Question

41. Sides of a triangle are given as 7 cm, 24 cm and 25 cm. Verify whether the triangle is
right triangle.
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Answer 1

Solution

Given :-

• Side of triangle are 7 cm, 24 cm, 25 cm

Prove :-

• This triangle is a right triangle

Explanation

Let, a ∆ ABC .

Where,

• AB = 7 cm
• BC = 24 cm
• CA = 25 cm

According to this,

• Longest side of triangle be = CA = 25 cm

Squaring both side

==> CA² = 25²

==> CA² = 625 cm².

Now, Calculate squar of other side

==> AB² = 7²

==> AB² = 49 cm²

And,

==> BC² = 24²

==> BC² = 576

According to Pythagoras theorem,

$\boxed{\underline{\tt{\orange{\:(Hypotenuse)^2\:=\:(Perpendicular)^2+(Base)^2}}}}$

Where, we let

• Hypotenuse = CA
• Perpendicular = AB
• Base = BC

So, Now Calculate

==> CA² = AB ² + BC²

keep all above Values

==> 625 = 49 + 576

==> 625 = 625

==> L.H.S. = R.H.S.

This, follow Pythagoras theorem

Hence

• There are the side of a right triangle

That's proved.

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