Question

kalas vegetable garden has an area of 300 ft². it is the shape of a rectangle with a length of 30 ft and a width of 10 ft. she has decided to expand the garden to make room for several new varieties of lettuce. the new garden will be a larger rectangle. she plans on making the new length 2 times the current length and the new width 5 times the current width.
(a) fill in the blanks to describe the size of kalas new garden.
new length × new width = new area
□ ft × □ ft = □ ft²
(b) how will the expansion change the area of the garden?
the area of the new garden will be □ times the area of the current garden.
(c) kalas friend jim also wants to expand his rectangular garden. jim wants his new garden to be a rectangle that has 28 times the area of his current garden. he goes to kala for advice. fill in the blank so that kalas advice to jim is correct.
make the new length 7 times the current length, and make the new width □ times the current width.

Explanation:

Step1: Calculate new length and width for part (a)

Current length \( l = 30\) ft. New length \(L=2\times30 = 60\) ft.
Current width \(w = 10\) ft. New width \(W = 5\times10=50\) ft.
New area \(A = L\times W=60\times50\)

Step2: Calculate new area for part (a)

\(60\times50=3000\)

Step3: Find the multiple for part (b)

Current area \(A_{old}=300\) ft², new area \(A_{new} = 3000\) ft².
\(\frac{A_{new}}{A_{old}}=\frac{3000}{300}=10\)

Step4: Let the multiple of width be \(x\) for part (c)

Let original length be \(l\) and original width be \(w\). Original area \(A = l\times w\). New length \(L = 7l\), new width \(W=xw\). New area \(A_{new}=28A\).
Since \(A_{new}=L\times W=(7l)\times(xw)\) and \(A = l\times w\), then \(7x\times(lw)=28(lw)\). Divide both sides by \(lw\) (assuming \(l
eq0\) and \(w
eq0\)), we get \(7x = 28\), so \(x=\frac{28}{7}=4\)

Answer:

(a) \(60\) ft \(\times50\) ft \(=3000\) ft²
(b) \(10\)
(c) \(4\)