Question

Find all sides of a right triangle whose perimeter is equal to 60 cm and its area is equal to 150 square cm. ​

Answer 1

x + y + H = 60 : perimeter , x, y and H be the two legs and the hypotenuse of the right triangle

(1/2)xy = 150 : area

x2 + y2 = H2: Pythagora's theorem.

3 equations with 3 unknowns.

(x + y)2 - 2xy = H2 : completing the square in the third equation.

x + y = 60 - H : express x + y using the first equation and use the second equation to find xy = 300 and substitute in equation 5.

(60 - H)2 - 600 = H2 : one equation with one unknown.

Solve for H to find H = 25 cm. Substitute and solve for x and y to find x = 15 cm and y = 20 cm.

Answer 2

Answer:

Step-by-step explanation:Area of right angle triangle=150cm^2

1/2*base*height=150

b*h=300

sum of sides=perimeter

b+h+√b²+h²=60

b+h+√(b+h)²-2×b×h=60

let b+h=x

⇒x+√x²-600=60

⇒√x²-600=60-x

⇒x²-600=(60-x)²

⇒x²-600=3600+x²-120x

⇒120x=4200

x=4200/120

x=35

b+h=35

so (b-h)²=(b+h)²-4bh

⇒(b-h)²=1225-1200

⇒b-h=5

so base=20

height=15

hypotenuse=25 ans