Question

if the ratio of the base andthe hypotaneous of right angled triangle 4:5,and the perimeter of the trangle is 48 cm find its area

Answer 1

Answer:

Step-by-step explanation:

ratio of the base andthe hypotaneous of right angled triangle 4:5

let say base = 4x

then hypotaneous = 5x

height^2 = hypotaneous^2 - base^2

height^2 = (5x)^2 -(4x)^2

height^2 = 15x^2 -16x^2

height^2 = 9x^2

height^2 = (3x)^2

height = 3x

petimeter = 3x + 4x + 5x

perimeter = 12x

12x = 48 cm

x = 4cm

area = (1/2)*(base*height)

=(1/2)(4x)(3x)

= 6x^2

= 6*(4)^2

= 6* 16

= 96 cm^2

Answer 2

let base be 4x and hypotenuse be 5x

by pythagoras theorem,

perpendicular = √((5x)²-(4x)²) = √(25x²-16x²) = √(9x²) = 3x

perimeter = base + hypotenuse + perpendicular

⇒ 48 = 4x + 5x + 3x

⇒ 48 = 12x

⇒ x = 48/12

⇒ x = 4cm

∴ base = 4x = 4*4 =16 cm

  hypotenuse = 5x = 5*4 = 20 cm

  perpendicular = 3x = 3*4 = 12 cm

Area =(1/2)*base*perpendicular

        =(1/2)*16*12

        =96 cm²

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