The area of a playground is 168 ๐ฆ๐2. The width of the playground is 2 ๐ฆ๐ longer than its length. Find the length and width of the playground. Then, enter the sum of the length and width in the provided grid.
please help
W = L+2
area = LW = L(L+2) = 168
L=12, W=14
thank you
To solve this problem, we'll need to set up an equation. Let's assume that the length of the playground is ๐ฅ ๐ฆ๐.
We're given that the width of the playground is 2 ๐ฆ๐ longer than its length. So, the width would be ๐ฅ ๐ฆ๐ + 2 ๐ฆ๐.
The area of a rectangle is calculated by multiplying its length and width. In this case, the area is given as 168 ๐ฆ๐ยฒ. So, we can set up the equation:
๐๐๐๐๐กโ = ๐๐๐๐๐กโ(๐ฅ) ร ๐ค๐๐๐กโ(๐ฅ)
168 ๐ฆ๐ยฒ = ๐ฅ ๐ฆ๐ ร (๐ฅ ๐ฆ๐ + 2 ๐ฆ๐)
Let's solve this equation and find the values of ๐ฅ:
168 ๐ฆ๐ยฒ = ๐ฅยฒ ๐ฆ๐ยฒ + 2๐ฅ ๐ฆ๐ยฒ
168 ๐ฆ๐ยฒ - ๐ฅยฒ ๐ฆ๐ยฒ - 2๐ฅ ๐ฆ๐ยฒ = 0
168 - ๐ฅยฒ - 2๐ฅ = 0
We can then factorize this quadratic equation:
-๐ฅยฒ - 2๐ฅ + 168 = 0
-1(๐ฅยฒ + 2๐ฅ - 168) = 0
(๐ฅ - 12)(๐ฅ + 14) = 0
Setting each factor equal to zero, we can solve for ๐ฅ:
๐ฅ - 12 = 0, which gives ๐ฅ = 12
๐ฅ + 14 = 0, which gives ๐ฅ = -14 (disregarding this negative value since it's not relevant here)
So, the length of the playground is 12 yards. Since the width is 2 yards longer, the width would be 12 + 2 = 14 yards.
To find the sum of the length and width, we add 12 + 14:
12 + 14 = 26
The sum of the length and width of the playground is 26 yards.