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2 years ago

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The expression below represents the perimeter, in feet, of Manual’s garden. 15 + 2x + 7 + 15 + 2x + 7 Use exactly two terms to w

rite an equivalent expression to represent the perimeter, in feet, of Manual’s garden. The area, measured in square feet, of Manual’s garden is found by calculating 15(2x + 7). Manual incorrectly says the area can also be found using the expression 30x + 7. Describe the error in Manual’s expression. Also, find the difference, in square feet, between the actual area of Manual’s garden and the area found using his expression as a part of your explanation. Manual’s friend Sasha designs a square garden. Each side measures 3x + 5 in length. The perimeter of Sasha’s garden is how much larger than the perimeter of Manual’s garden?

1 answer:

astraxan [27]2 years ago

7 0

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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