Question

Area of triangle 150cm and its sides are respectively 3:4:5 what is the perimeter

Answer 1

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Ratio of sides = 3:4:5

Let the sides be 3x, 4x and 5x.

But, 1 min,...

First we have to find which type of triangle is this.

It seems that,

(3x)² + (4x)² = 9x² + 16x² = 25x² = (5x)²

⇒ (3x)² + (4x)² = (5x)²

Which means, the square of the largest side is equal to the sum of the squares of the other sides, i.e., Pythagoras' theorem.

So it is a right triangle!

We know that the area of a right triangle is half of the product of the perpendicular sides.

Here the hypotenuse is 5x. So the other sides 3x and 4x are the perpendicular sides.

∴ 1/2 × 3x × 4x  =  150

⇒ 1/2 × 12x²  =  150

⇒ 6x²  =  150

⇒ x² = 25

⇒ x = 5

So we got the value of x. So let's find the perimeter.

Perimeter

= 3x + 4x + 5x

= 12x

= 12 × 5

= '60 cm'

∴ Perimeter is 60 cm.

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