Question

A right angled triangle has its area numerically equal to its perimeter the length of each side is an even number and the hypotenuse is 10cm what is the perimeter of the triangle

Answer 1

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Answer 2

Answer:

The perimeter of the triangle is 24 cm.

Step-by-step explanation:

Given : A right angled triangle has its area numerically equal to its perimeter the length of each side is an even number and the hypotenuse is 10 cm.

To find : What is the perimeter of the triangle?

Solution :

A right angle triangle ABC,

Each side is an even number,

Let the Perpendicular of the triangle, AB=2x

Let the Base of the triangle, BC=2x+2

Hypotenuse given AC=10 cm.

According to question,

$AB+BC+CA=\frac{1}{2}\times BC\times AB$

$2x+2x+2+10=\frac{1}{2}\times (2x+2)\times (2x)$

$4x+12=x(2x+2)$

$2x^2-2x-12=0$

$x^2-x-6=0$

$x^2-3x+2x-6=0$

$x(x-3)+2(x-3)=0$

$(x+2)(x-3)=0$

$x=-2,x=3$

Since,We take x=3

Sides of triangle is AB=2*3=6 cm

BC=2(3)+2=8 cm

AC=10 cm.

Perimeter of the triangle is

P= AB+BC+CA

P= 6+8+10

P=24 cm.

Therefore, The perimeter of the triangle is 24 cm.