The perimeter of Sasha’s garden is 8x - 24 larger than the perimeter of Manual’s garden
<h3>The equivalent expression using exactly two terms </h3>
The perimeter is given as:
P = 15 + 2x + 7 + 15 + 2x + 7
Collect like terms
P = 2x + 2x + 7 + 15 + 15 + 7
Evaluate the like terms
P = 4x + 44
<h3>The area of the garden</h3>
The area of the garden is given as:
A = 15(2x + 7).
Expand
A = 30x + 105
Manual's expression of the area is 30x + 7
Hence, Manuel's error is that he did not multiply 15 by 7 when expanding the bracket and the actual area is 30x + 105
<h3>The difference between the areas of Manual’s garden and Sasha's design</h3>
The side length of Sasha's design is:
L = 3x + 5 in
So, the area is:
A = (3x + 5)^2
Expand
A = 9x^2 + 16x + 25
The difference between both areas is:
Difference = 9x^2 + 16x - 30x + 25 - 105
Evaluate
Difference = 9x^2 - 14x - 80
Hence, the difference between the areas of Manual’s garden and Sasha's design is 9x^2 - 14x - 80
<h3>The perimeter of Sasha's garden</h3>
This is calculated using:
P = 4L
So, we have:
P = 12x + 20
The difference between both perimeter is:
Difference = 12x - 4x + 20 - 44
Evaluate
Difference = 8x - 24
Hence, the perimeter of Sasha’s garden is 8x - 24 larger than the perimeter of Manual’s garden
Read more about area and perimeter at:
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