Question

Right angle triangle having perimeter 120 CM has its two perpendicular sides in the ratio 5 is to 12 find the length of its sides

Answer 1

using Pythagoras theorem
we can find the ratio of remaining side
let x be common multiple
so, side one 5X its perpendicular side 12X
$5 x{}^{2} + 12x {}^{2} = 13x {}^{2}$
from this ratio of third side is 13X
now,
$5x + 12x + 13x = 120$
$30x = 120$
$x = 4$
put value of X in the ratio
5X= 5×4=20
12X=12×4=48
13X=13×4=52
therefore value of two perpendicular side is 20 and 48

Answer 2

let, two perpendicular sides are 5x and 12x

then,

hypotenuse = √{(5x)^2 + (12x)^2}

=√(25x^2 + 144x^2)

=√(169x^2)

=13x

now,

13x + 12x + 5x = 120

=> 30x = 120

=> x = 120/30 = 4

hence, lengths of its sides are:-

5x =5×4 =20 cm

12x =12×4 =48 cm

13x =13×4 =52 cm

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I hope this will help you..