Question

If all the sides of a triangle are in the ratio 5:3:4 prove that it is a angle triangle​

Answer 1

CORRECT QUESTION :-

★ If all the sides of a triangle are in the ratio 5:3:4 . Prove that it is a right angled triangle.

GIVEN :-

• all the sides of a triangle are in the ratio 5:3:4 .

TO PROVE :-

• The triangle is a right angled triangle.

SOLUTION :-

Let the ratio constant be "x".

★ sides of a triangle are in the ratio 5x , 3x , 4x.

As we know that in Pythagoras theorem the the sum of square First side is equal to the sum of square of other two sides. i.e (Hypotenuse)² = (perpendicular)² + (Base)².

★ BY PYTHAGORAS THEOREM ★

→ (5x)² = (3x)² + (4x)²

→ 25x² = 9x² + 16x²

→ 25x² = 25x².

Here the Pythagoras theorem is the theorem which is always used in right angled triangle. There by Pythagoras theorem we proved that the triangle is a right angled triangle.

HENCE PROVED ✅

Answer 2

Correct Question :-

• If all the sides of a triangle are in the ratio 5 : 3 : 4 prove that it is a right angled triangle.

Answer with explanation :-

Given :-

• A triangle are in the ratio 5 : 3 : 4

To Prove :-

• That it is a right angled triangle

Solution :-

Let,

• The ratio constant be ‘x’

The sides of angles are,

• 5x
• 3x
• 4x

We know that,

$\boxed{\sf(Hypotenuse)^{2} = (Perpendicular)^{2} + (Base)^{2}} \: \: ( \bf Pythagoras\:theorem )$

Substituting the values we get,

$:\implies\sf (5x)^{2} = (3x)^{2} + (4x)^{2}$

$:\implies\sf25x^{2} = 9x^{2} + 16x^{2}$

$:\implies\sf25x^{2} = 25x^{2}$

There by, Pythagoras theorem we prove that traingle is a right angled triangle.

HENCE PROVED