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
Answers
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
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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