Question

A boardwalk is 1/4 of a rectangle which has length of 20m and a width of 12m.
1) Formulate an algebraic expression for the total area of the boardwalk given that the width of the boardwalk is unknown.
2) Form an algebraic equation with only one unknown for the total area of the boardwalk.
3) Express the equation in question 2 in the form of (x-a)(x-b)=0

Answer 1

hint:
what is the area of the rectangle?

Answer 2

The area of the rectangle is 240m.

Answer 3

ok! Now the area of board walk is:
240:4=...?

Answer 4

60 ??

Answer 5

yes!

Answer 6

But how do we formulate an algebraic equation ?

Answer 7

please wait a moment, I'm checking my formulas...

Answer 8

Sure.

Answer 9

for question 1), we can assume that the length of our boardwalk is 20 meters, so the width is unknown. Now I call with W the width of our boardwalk, then the product
W*20 has to be equal to?

Answer 10

I have my answer as 1/4(20W) = 60m

Answer 11

from your equation I get:
20*W = 240, is it right?

Answer 12

Yes

Answer 13

The total area of the boardwalk is known to be 1/4 of the area of the rectangle.

Answer 14

yes! nevertheless the area of our boardwalk has to be 60 m^2

Answer 15

Yup ^^

Answer 16

for question 2) we have to find 2 numbers such that their sum is equal to the halfperimeter of our rectangle, namely (20+12)*2/2= 32, and their product has to be equal to
(20*12)/4 = 60. What is that equation?

Answer 17

since we have to write a quadratic equation

Answer 18

furthermore a rectangle whose sides are:
Length = 20/2 = 10 meters
and
width = 12/2 = 6 meters
has its area equal to 60 m^2, namely equal to 240/4

Answer 19

do you know how to write that equation?

Answer 20

Nope. Maybe I will just have to ask my school teacher tomorrow. Thanks for your effort :)

Answer 21

thanks! :)