Question

You are helping Bobby find the length and width of his garden. He knows that the area of the garden is LaTeX: x^2+8x+15x 2 + 8 x + 15 square feet. The length of his garden is LaTeX: \left(x+5\right)( x + 5 )square feet.

Part 1) What is the width of the garden? Explain how you came to this conclusion and what method you used (algebra tiles, the x-method, another method, etc. )

Part 2) If LaTeX: xx is 3 feet, what would the area of the garden be? Show your work.

Answer 1

If the length of the garden is (x + 5) then the width will be (x + 3)

The area of the garden is 48 sq feet

Explanation:

The garden is x^2 + 8x + 15 sq feet

Use the factorization method and break the middle term:

x^2+3x+5x+15

Group the first two terms and last two terms:

(x^2+3x)+(5x+15)

Take out the common from each pair.

x(x+3) +5(x+3)

(x+5)(x+3)

We have already been given that x+5 is the length. Then this shows that x+5 is the length and x+3 is the width

If the length of the garden is (x + 5) then the width will be (x + 3)

The method I used is the F.O.I.L. method

The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial. Then Outer means multiply the outermost terms in the product.

(x + 5)(x + 3) = x^2 + 3x + 5x + 15

Solve the like terms:

= x^2 + 8x + 15

b) x= 3 feet

(x + 5)(x + 3)

Substitute the value in the expression

(3 + 3)(5 + 3)= (8)(6)= 48 square feet

Area of the garden is 48 sq feet.