Question

if in a right angled triangle in which perimeter is 60cm and hypotenus is 25 cm find its area

Answer 1

Answer:

 

Step-by-step explanation:

 

Perimeter of right angle triangle = 60 cm

Let the triangle be ∆ ABC ,

AB = Perpendicular

BC = Hypotenuse

AC = Base

Now

AB + BC + CA = 60

AB + 25 + CA = 60

AB + CA = 35

AB = (35 - CA)

BC = 25 cm (given)

AB² + AC² = BC²

AB² + AC² = 25²

AB² + AC² = 625

Put the value of AB

(35 - CA)² + AC² = 625

35² + AC² - 2×35×AC + AC² = 625

1225 + 2AC² - 70AC = 625

2AC² - 70AC + 1225 - 625 = 0

2AC² - 70AC + 600 = 0

AC² - 35AC + 300 = 0

AC² - 20AC -15AC + 300 = 0

AC(AC - 20) - 15(AC - 20) = 0

(AC - 15) (AC - 20) = 0

AC = 15,20

AB = Perpendicular = 20 cm

BC = Hypotenuse = 25 cm

AC = Base = 15 cm

Perimeter = 15 + 25 + 20 = 60 cm

$Area \: = \: \dfrac{1}{2}\times Base \times Height$

$Area \: = \: \dfrac{1}{2}\times 15 \times 20$

$Area \: = \: 15\times 10$

$\boxed{\boxed{Area \: = \: 150 \: cm^{2}}}$