Sharon has a patio in the shape of a rectangle. • The length of the patio is feet. l The width of the patio is feet w . Sharon plans to expand the patio by increasing the length by 50% and increasing the width by 20% . a (1.5l)(1.2w) b(l+0.5)x(w_0.2) c (l x w )+(0.5+0.2) d (0.5l) x (0.2w)

Answer 1

To determine the new dimensions of Sharon's patio after the planned expansions, we need to adjust the length and width based on the percentages given:

1. Increasing the length by 50%:

   • The new length will be \(l + 0.5l = 1.5l\).

2. Increasing the width by 20%:

   • The new width will be \(w + 0.2w = 1.2w\).

Next, if we want to find the area of the expanded patio, we multiply the new length and width:

• New area = \( (1.5l)(1.2w) \).

Now, let's analyze the options given:

a) \((1.5l)(1.2w)\) — This correctly represents the area of the expanded patio.

b) \((l + 0.5)(w - 0.2)\) — This is incorrect because it does not properly increase the length and width as specified.

c) \((l \times w) + (0.5 + 0.2)\) — This incorrectly adds the percentages rather than calculating the dimensions.

d) \((0.5l) \times (0.2w)\) — This calculates a product of half the length and a fifth of the width, which is not applicable here.

Therefore, the correct representation of the area of the expanded patio is option a: \((1.5l)(1.2w)\).