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 104cm104cm. The minor cathetus is 3/53/5 of hypotenuse. Calculate the perimeter and area of ​​the triangle?