Exercise 4 Page 213

Let w be the width and l be the length of the vegetable garden. Since the length of the garden is 15 times its width, we can write an equation to relate these two values. l=15w In order to find the area of the garden, we need to know the actual values of the length and width. We can find them using the fact that the perimeter of the garden is 160 ft. The perimeter of a rectangle can be calculated by adding all four of the side lengths. P=2w+2lSubstituting 160 for P and 15w for l into the formula, we get an equation for w. Let's solve it!

P=2w+2l

SubstituteII

P= 160, l= 15w

160=2w+2( 15w)

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Solve for x

Multiply

Multiply

160=2w+30w

AddTerms

Add terms

160=32w

DivEqn

.LHS /32.=.RHS /32.

5=w

RearrangeEqn

Rearrange equation

w=5

The width of the garden is 5 ft. Let's use this piece of information, and the relation we found earlier, to calculate the length. 15w=l ⇒ 15( 5)=75 Now that we know both the length and the width of the garden, we can calculate its area. We will use the formula for the area of a rectangle. A=l w Let's substitute 75 for l and 5 for w, and solve the equation for A.

A=l w

SubstituteII

l= 75, w= 5

A= 75( 5)

Multiply

Multiply

A=375

The area of the vegetable garden is 375ft^2. The answer is G.