In a right-angled triangle the sum of the minor cathetus and the hypotenuse is 104 cm. The minor cathetus is 35 of hypotenuse. Calculate the perimeter and area of the triangle?

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ringbarsh1i

2022-02-12

In a right-angled triangle the sum of the minor cathetus and the hypotenuse is 104 cm. The minor cathetus is

\frac{3}{5}

of hypotenuse. Calculate the perimeter and area of the triangle?

Morgan Griffin

Beginner2022-02-13Added 9 answers

Step 1
As the minor cathetus is

\frac{3}{5}

of hypotenuse, let hypotenuse be 5x and then cathetus will be 3x and major cathetus will be

\sqrt{{(5 x)}^{2} - {(3 x)}^{2}} = \sqrt{25 x^{2} - 9 x^{2}} = \sqrt{16 x^{2}} = 4 x

As sum of the minor cathetus and the hypotenuse is 104 cm, we have

5 x + 3 x = 104

8 x = 104

x = 13

Hence perimeter of triangle will be

5 x + 3 x + 4 x = 12 x = 12 \times 13 = 156

cm
Area of triangle would be

4 x \times 3 x - 12 x^{2} = 12 \times 13 \times 13 = 2028 c m^{2}

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