Question

The Perimeter of a Triangle is 60 cm. It's Hypotenuse is 26 cm,Find the other Two sides and the area of the Triangle.......


Plz help!!!!!!!!!!!!!

Answer 1

Let the two sides of the triangle be b and h.

Given that perimeter of a triangle = 60cm.

Given that hypotenuse = 26cm.

b + h + 26 = 60

b + h = 60 - 26

b + h = 34.


We know that In a right-angled triangle c^2 = a^2 + b^2

b^2 + h^2 = 676

b^2 + (34 - b)^2 = 676

b^2 + 1156 - 68b + b^2 = 676

2b^2 - 68b + 1156 = 676

2b^2 - 68b + 480 = 0

b^2 - 34b + 240 = 0

b^2 - 24b - 10b + 240 = 0

b(b - 24) - 10(b - 24) = 0

b = 24, 10.

Then h = 34 - b

            = 34 - 24

             = 10.

h = 34 - b

   = 34 - 10

   = 24


Therefore the sides of a triangle = 24 and 10.

Now,

Area of triangle = 1/2 * b * h

                           = 1/2 * 24  * 10

                           = 120cm^2.


Therefore the area of triangle = 120cm^2.


Hope this helps!

Answer 2

Hi,

Please see the attached file!

Thanks