Question

The difference of length of two sides forming right angle in right angled triangle is 3 cm . the perimeter is 36 . find the area of the triangle​

Answer 1

Answer:

Step-by-step explanation:

Difference of  lengths of sides forming right angle in right angled triangle = 3cm

Perimeter of the triangle = 36 cm.

Let the length of the right angled triangle forming the right angle = x

Thus, the other side of right angled triangle will be= (x+3)

Using the pythagoras theorem we will get -  

h² = p²+b²  

where, Perpendicular = (x),  Base = (x+3),  and Hypotenuse (33-2x)

= (33-2x)² = (x+3)²+(x)²

= 4x² - 132x+1089 =x²+9+6x+x²

= 4x²- 2x²-132x-6x+1089-9 =0

= 2x²-138x+1080 = 0

= 2(x²-69x+540) = 0

Thus, x²-69x+540= 0

On solving the quadratic equation -  

x(x-60)-9(x-60)=0

(x-60)(x-9)=0

x = 60 or 9

Thus, length of sides when x = 9 = 9, 12,15

Answer 2

Answer:

In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation".

I hope this will be help you.