Courses
Courses for Kids
Free study material
Free LIVE classes
More LIVE
Join Vedantu’s FREE Mastercalss

# The perimeter of a right triangle is 60 cm. Its hypotenuse is 25 cm. Find the area of the triangle. Verified
361.8k+ views
Hint: In a Right-angled triangle, the square of the hypotenuse side is equal to the sum of the other two sides and the area of the triangle is half of its product of base and height.

Let, ABC be the given right angled triangle such that base $= BC = x{\text{ }}cm$ and hypotenuse $AC = 25cm$ . Perimeter is given to us as $60cm$ . Then,
$AB + BC + AC = 60 \\ \Rightarrow AB + x + 25 = 60 \\ \Rightarrow AB = 35 - x \\$
$A{B^2} + B{C^2} = A{C^2} \\ \Rightarrow {(35 - x)^2} + {x^2} = {25^2} \\ \Rightarrow 1225 + {x^2} - 70x + {x^2} = 625 \\ \Rightarrow 2{x^2} - 70x + 600 = 0 \\ \Rightarrow {x^2} - 35x + 300 = 0 \\ \Rightarrow {x^2} - (15 + 20)x + 300 = 0 \\ \Rightarrow {x^2} - 15x - 20x + 300 = 0 \\ \Rightarrow x(x - 15) - 20(x - 15) = 0 \\ \Rightarrow (x - 20)(x - 15) = 0 \\ \Rightarrow x = 15,20 \\$
If, $x = 20{\text{ then }}AB = 35 - x = 35 - 20 = 15{\text{ and }}BC = x = 20$ .
Area of a triangle can be calculated by $\dfrac{1}{2}(base \times height)$ so, $\dfrac{1}{2}(BC \times AB) = \dfrac{1}{2}(15 \times 20) = 150c{m^2}$ .