Question

two legs of a right angled triangle are in ratio of 3:4find the shortest leg if the hupotenuse is 75cm

Answer 1

let the two legs of right angled triangle be 3x and 4x respectively

hypotenuse = 75cm

according to question ,

using Pythagoras theorem ,
sum of square of two legs = hypotenuse²

=> (3x)²+(4x)² = (75)²
=> 9x²+16x² = 5625

=> 25x² = 5625

=> x² = 5625/25 => 225

x²= 225
=> x = √225 = 15


sides of Right angled triangle = 3x = 3(15) = 45 cm

and 4x = 4(15) = 60 cm


shortest side = 45 cm


hope this helps

Answer 2

Let the base be the shortest side and its ratio be 3x
Let the perpendicular be 4x
Hypotenuse is 75cm
By pythagorus theorem
B^2+P^2=H^2
(3x)^2+(4x)^2=75^2
9x^2+16x^2=5625
25x^2=5625
x^2=5625/25
x^2=225
x=15
3x=3×15=45
Hence the shortest side is 45 cm long