Question

the area of right angled triangle is 40 cm2 and perimeter is 40 cm the length of its hypotenuse is explain the answer

Answer 1

Let the base be 'x'
Height be 'y'
Hypotenuse be 'z'
Area of a right angle triangle=1/2*base*height
40=1/2*x*y
80=xy

Perimeter=x+y+z
40=x+y+z
40-z=x+y

We know that
x^2+y^2=z^2
(a+b)^2=a^2+b^2+2ab
a^2+b^2=(a+b)^2-2ab
So we get
(x+y)^2-2xy=z^2
(40-z)^2-2(80)=z^2
1600-80z+z^2-160=z^2
1440-80z=0
1440=80z
z=1440/80=18 cm
Hypotenuse=18cm