Question

the perimeter of a right triangle is 24cm if its hypotenuse is 10cm then find its area

Answer 1

Hey mate here is your answer

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

hope this answer is helpful for you

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Answer 2

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