Question

Question 12Sophia wants to plant a garden that will be in the shape of arectangle. She was given 80 feet of fencing to enclose the garden(perimeter). She wants the length to be 10 feet more than twicethe width. What are the dimensions, in feet, of Sophia's garden ifshe uses all 80 feet of fencing?

Answer 1

EXPLANATION

Let's see the facts:

Sophia's garden shape: rectangular

The perimeter of the garden = 80 ft (conditional)

Length = 10+2Width ---> l = 10+2w (conditional)

As we can see, there are two variables and two equations, so we must solve this system of equations:

(1) p = 2 (w+l) = 80 (Perimeter Formula)

(2) l = 10 + 2w (Conditional)

Now, we can solve (1) equation and replace in (2):

80 = 2w + 2l (Isolating w)

80 - 2l = 2w (Dividing both sides by 2)

40 - l = w

Now, replacing in (2):

l = 10 + 2(40-l) (Applying distributive property)

l = 10 + 80 - 2l (Adding +2l to both sides and simplifying)

3l = 90 (Dividing both sides by 3)

l = 30

Now, we have l=30, so with this variable can calculate w in this way:

w = 40 - l = 40 - 30 = 10

w = 10

Now we have the dimensions: Width=10ft and Length= 30ft

[ANSWER] The dimensions are: Width=10 feet and Length= 30 feet