Question

A mini basketball court has an area of 500

square feet and a perimeter of 90 feet.
- what are the dimensions of the court?

Answer 1

20 by 25 feet

Explanation:

A = L·w

P = 2L + 2w

500 = Lw

90 = 2L + 2w

we could solve the first equation for 'w' and then substitute that value into the second equation:

w = 500/L

90 = 2L + 2(500/L)

90 = 2L + 1000/L

90 = (2L² + 1000)/L

multiply each side by L to eliminate it as the denominator

90L = 2L² + 1000

2L² - 90L + 1000

the zeros of this quadratic are 20 and 25

A = 20 x 25 which equals 500

P = 2(20) + 2(25) which equals 90

Answer 2

Explanation:

let x,y be the sides of court.

2(x+y)=90

x+y=90/2=45

y=45-x

xy=500

x(45-x)=500

45x-x²=500

x²-45x+500=0

x²-25x-20x+500=0

x(x-25)-20(x-25)=0

(x-25)(x-20)=0

x=25,20

when x=25

y=45-x=45-25=20

when x=20

y=45-20=25

sides are 25 ft,20 ft.