In a right-angled triangle the sum of the minor cathetus and the hypotenuse is #104cm#. The minor cathetus is #3/5# of hypotenuse. Calculate the perimeter and area of the triangle?

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Answer 1 · 2016-04-19T10:03:02

Perimeter of triangle is #156# #cm# and rea of triangle is #2028# #cm^2#.

As the minor cathetus is #3/5# of hypotenuse, let hypotenuse be #5x# and then cathetus will be #3x# and major cathetus will be

#sqrt((5x)^2-(3x)^2)=sqrt(25x^2-9x^2)=sqrt(16x^2)=4x#

As sum of the minor cathetus and the hypotenuse is #104# cm, we have #5x+3x=104# or #8x=104# or #x=13#.

Hence perimeter of triangle will be #5x+3x+4x=12x=12xx13=156# #cm#.

Area of triangle would be #4x xx3x=12x^2=12xx13xx13=2028# #cm^2#.

In a right-angled triangle the sum of the minor cathetus and the hypotenuse is #104cm#. The minor cathetus is #3/5# of hypotenuse. Calculate the perimeter and area of ​​the triangle?