A rectangular garden is 5 ft longer than it is wide. Its area is 750 square feet. What are its dimensions?

Question

its width equals:

its length equals: 

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is to find a way to relate the quantities of a rectangle to one another. On this one we have

Area = L x W = 750

L = W + 5  because it’s 5 feet longer than it is wide

I would plug the second equation into the first to get

(W + 5)(W) = 750

W^2 + 5W – 750 = 0

(W + 30)(W – 25) = 0

W = -30 or W = 25 … only 25 makes sense in this context since we need a positive value because the value is a length

So Width = 25, then Length = W + 5 = 25 + 5 = 30

The dimensions here are 25 feet wide by 30 feet long

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

another solution...

750=10*75

750=2*5*3*5*5

750=(2*3*5)*(5*5)

750=30*25 and 30 is 5 more than 25

dimensions are 25 by 30

Answer 3

Area= length X Width

 

let the width = w

length is 5ft longer than the width= w+5

Area=750

 

substitute in the equation: 750=(w+5).(w)

                                       750=w²+5w

factorize the equation: w²+5w-750=0

                                 (w+30)(w-25)=0

                                 w=-30 and w=25 therefore the width is 25 and the length is w+5=25+5=30

 

Answer 4

l * w = area = 750

l = w+5

 

(w+5)*w = 750

w^2 + 5w - 750 =0

(w+30)(w-25) = 0

 

w = -30 or 25 but since area can't be negative we know it must be 25

 

l = 25+5 = 30

 

Plug back into equation 1 to check.

 

30 * 25 = 750

750=750