Question

if the ratio of the base and hypotenuse of a right angle triangle if 4:5 and the perimeter is 48 cm, find its area

Answer 1

hope it helps to u........

Answer 2

Let ABC is a right triangle.

Base = BC = 4x

Hypotenuse = AC = 5x

As we know that,


=> (AC)^2 = (AB)^2+(BC)^2

=> (5x)^2 = (4x^2) + (BC)^2

=> 25 x^2 = 16 x^2 +(BC)^2

=> (25-16) x^2 = (BC)^2

=> BC^2 = 9x^2

=> BC^2 = (3x)^2 [ Both Exponential powers will cancel eachother].

=> BC = 3x

=> Perimeter = 48 cm (given)

=> 3x + 4x + 5x = 48 cm

=> 12x = 48 cm

=> x = 48/12 cm

=> x = 4 cm

Again,

Altitude = 3x = 12 cm
Base = 4x = 16 cm
Hypotenuse = 5x = 20 cm

As we know that,


=> Area of triangle = 1/2 x Base x Height or Altitude

=> Ar( ABC) = (1/2 x 16 x 12) cm^2

=> Ar( ABC) = 96 cm^2






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