Question

The perimeter of a right angle triangle is 24cm and Hipotenus is 10cm find area of atriangle

Answer 1

Given the perimeter = 24 cm

The hypotenuse = 10

Then we know that the perimeter of the triangle is the sum of all three sides:

Let the sides be x , y , and the hypotenuse = 10

==> x + y + 10 = 24

==> x + y = 14

==> x = 14 - y  ............(1)

Also we know that:

 x^2 + y^2 = 10^2

==> x^2 + y^2 = 100 .............(2)

now we will substitute (1) in (2):

==> (14-y)^2 + y^2 = 100

==> 196 - 28y + y^2 + y^2 = 100

==?> 2y^2 - 28y + 196 = 100

==> 2y^2 - 28y + 96 = 0

Let us divide by 2:

==> y^2 -14y + 48 = 0

==> we will factor:

==> ( y - 8 ) ( y- 6)

==> y1= 8 ==> x1= 6

==> y2 = 8 ==> x2= 6

But given : x> y

==> x = 8   and y = 6

Answer 2

Perimeter =24
3a. =24
a. =24/3
=8cm

Area =1/2* base*height
=1/2 *8*10
=40cm
Hope it helps you