Given:

Perimeter of right triangle = 56 cm

Hypotenuse = 25 cm


To find:

Other two sides

Area of the triangle using formula for a right triangle

Verification of the answer using Heron's formula




Let the other two sides of the right triangle be a and b respectively.

We know that the sum of all sides of a triangle is equal to its perimeter.

Therefore, a + b + 25 = 56

a + b = 31


We also know that in a right triangle, the sum of the squares of the other two sides is equal to the square of the hypotenuse.

Therefore, a² + b² = 25²

a² + b² = 625


Solving the above two equations simultaneously, we get:

a = 20 cm

b = 11 cm


Now, we can find the area of the right triangle using the formula:

Area = 1/2 * base * height

As the given triangle is a right triangle, the base and height are the other two sides.

Therefore, Area = 1/2 * 20 cm * 11 cm = 110 cm²


To verify the answer, we can use Heron's formula which states:

Area of triangle = √(s(s-a)(s-b)(s-c))

where s = (a+b+c)/2 is the semi-perimeter of the triangle.


In this case, c is the hypotenuse and we have already found the values of a and b.

Therefore, s = (a+b+c)/2 = (20+11+25)/2 = 28


Now, substituting the values in Heron's formula:

Area = √(28(28-20)(28-11)(28-25))

Area = √(28*8*17*3)

Area = 110 cm²


Therefore, the area obtained using both formulas is the same and the answer is verified.




Heron's formula is used to find the area of a triangle whose sides are known. It is named after Hero of Alexandria, a Greek mathematician who first described the formula. The formula can be used for all types of triangles, whether they are acute, right, or obtuse. The formula is given as:

Area of triangle = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, and a, b, and c are the lengths of its sides. The semi-perimeter is half the sum of the lengths of all sides of the triangle, i.e., s = (a+b+c)/2. The formula can be used to find the area of any triangle, whether it is a right-angled triangle or not.