Find out the area of a right angled triangle, with a perimeter of 12 meters and a hypotenuse of 5 meters.  

Concept:

Pythagoras theorem:

(Hypotaneous)² = (Base)² + (Height)²

Area of a right angle triangle = \(\frac{1}{2}~\times~base~\times~height\)

Calculation:

Given:

Perimeter of the right angled triangle = 12 meters

hypotenuse of the right angled triangle = 5 meters

Let the base of the right angled triangle be 'b' and height be 'a'.

∵ Perimeter of a triangle = sum of its sides

⇒ 12 = a + b + 5

⇒ a + b = 7

⇒ a = 7 - b

Applying Pythagoras theorem to the right angled triangle:

(Hypotaneous)2 = (Base)2 + (Height)²

⇒ 5² = b² + (7 - b)²

⇒25 = b2 + 49 + b2 - 14b

⇒ (b−4)(b−3) = 0
Then we got the value of b as 4 and 3.
b=4, 3

a=7 − b
a=3, 4
For the two different values of b we will get two different values of a.

Then we can calculate the Area as:

Area = \(\frac{1}{2}~\times~base~\times~height\) = \(\frac{1}{2}~\times~3~\times~4\) = 6 m²