Question

You are playing miniature golf on the hole shown.

a. Write a polynomial that represents the area of the golf hole. Show your steps and explain how you found the polynomial.

b. Write a polynomial that represents the perimeter of the golf hole. Show your steps and explain how you found the polynomial.

Bonus:

c. Find the perimeter of the golf hole when the area is 216 square feet.

Answer 1

Explanation:

Hi Tiako, I like mini-golf :P let's play... the math of this is fun too

a)

there is the small square in the bottom left that is x * x or x^2

then there is the bigger rectangle that is (x+4) * 3x

A = x^2 + (x+4)*(3x)

A = X^2 + 3x^2 + 12x

A = 4x^2 +12x

b)

add up the sides

the small square on the lower left is 2x + 2x

the bigger rectangle on the right is 2(x+4) + 2*3x

P = 2x +2x +2(x+4) + 2*3x

P = 4x + 2x +8 + 6x

P = 12x +8

c)

use a) and set it to 216

216 = 4x^2 +12x

bring the 216 over with the x's to see if it's easy to factor

0 = 4x^2 +12x - 216

divide thru by 4

0 = x^2 + 3x - 54

hmmm can you see what it factors to?

6*9 = 54 and 9-6 = 3 .. so that seems like it

(x-6)(x+9)

x=6

x= -9

so it's either 6 or -9... since area can't be negative we toss -9 out and use 6 :P

x=6

now use b) with 6 plugged in for x

P = 12(6) + 8

P = 72 + 8

P = 80

Yay, hole in one ! :DDDD umm, or 80 ?

anyway, got it?