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alisha [4.7K]
3 years ago
14

A rectangle has an area of 72 square inches. The width of the rectangle is 6 inches. What is the length of the rectangle?

Mathematics
1 answer:
inn [45]3 years ago
3 0

Answer:

12

Step-by-step explanation:


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3 years ago
There are two buildings that you want to have in the amusement park, but the size hasn’t been determined yet. Although you don’t
Harrizon [31]
A) The area of a rectangle is A = lw, where l=length of the rectangle and w=width of the rectangle. You know the length of the gift shop, l = 20x + 24. You know the width, w = 36x - 20. Plug those expressions into the equation for area of a rectangle and multiply/foil:
A = lw\\&#10;A = (20x + 24)(36x - 20)\\&#10;A = (20x)(36x) + (20x)(-20) +  (24)(36x) + (24)(-20)\\&#10;A = 720x^{2} - 400x + 864x - 480\\&#10;A = 720x^{2} + 464x - 480

The expression for the area of the gift shop is 720x^{2} + 464x - 480.

B) The equation for the perimeter of the gift shop is P = 2(l+w), where l = length and w = width. Plug your values for l and w into this equation:
P = 2(l+w)\\&#10;P = 2(20x + 24 + 36x - 20)\\&#10;P = 2(56x + 4) = 2(56x) + 2(4)\\&#10;P = 112x + 8

The expression for the perimeter of the gift shop is 112x + 8

C) Since you know the perimeter is going to be 176 ft, that means P = 176. Plug that into the equation you found in part B, P = 112x + 8, and solve for x.
P = 112x + 8\\&#10;176 = 112x + 8\\&#10;112x =  168&#10;x = 1.5

Once you solve for x, you can plug x into your equations for width and length to find the dimensions. x = 1.5, so:
1) L<span>ength = 20x+24 feet 
</span>Length = 20(1.5) + 24 feet = 54 feet
2) Width = <span>36x-20 feet
Width = 36(1.5)-20 feet = 34 feet

Your dimensions are 54 feet (length) by 34 feet (width).
</span>
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3 years ago
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