Question

solve equation: a right angle triangle having perimeter 120cm has two perpindicular sides in ratio5:12 .find its lengths.

Answer 1

Let the perpendicular sides be 5x and 12x.

We know that (Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2

= > (Hyp)^2 = (5x)^2 + (12x)^2

= > (Hyp)^2 = 25x^2 + 144x^2

= > (Hyp)^2 = 169x^2

= > Hyp = 13x.

Now,

given perimeter = 120cm.

= > 5x + 12x + 13x = 120

= > 30x = 120

= > x = 4.

Hence,

Length of side 1 = 20.

Length of side 2 = 48.

length of side 3 = 52.

Therefore, the lengths are 20,48,52

Answer 2

given ,perimeter = 120 cm

ratio of two sides = 5:12

let the constant ratio be ' x '

so now sides are , 5x , 12x

third side will be = √ { ( 12x)^2 + ( 5x )^2 }

= √( 169x^2 )= 13x
now given ,perimeter = 120

5x + 12x + 13x = 120

30x = 120

x = 4

now the length of the sides of triangle are :

5x = 5× 4 = 20cm

12x = 12 × 4 = 48 cm

13x = 13 × 4 = 52 cm

therefore the lengths are , 20cm , 48cm and 52 cm.