Algebra 2 help?
2020-12-03 1:42 am
A rectangle and a square have the same area. The length of the rectangle is seventy feet more than two times its width. The length of a side of the square is thirty feet. What equation would help you solve for the dimensions of the rectangle? What are the dimensions of the rectangle?
回答 (2)
2020-12-03 2:05 am
✔ 最佳答案
L = 70 + 2WS = 30 ft
As = S²
As = 30² = 900 ft²
Ar = LW
As = Ar
LW = 900
(70 + 2W)W = 900
2W² + 70W - 900 = 0
If ax² + bx +c = 0
Then x = [-b ± √(b² - 4ac)] / 2a
W = -70 ± √(70² - 4(2)(-900)) / 2(2)
W = -70/4 ± (1/4)√(70² + 7200)
W = -70/4 ± 110/4
W = 10, -45
Throw out the meaningless result
W = 10 ft
L = 70 + 2(10)
L = 90 ft
2020-12-03 1:58 am
The area of the square is 30² (or 900 sq. ft).
The rectangle must have the same area.
Let w be the width (in feet)
Let 2w + 70 be the length (in feet)
The area is:
w(2w + 70) = 900
You could also expand that to:
2w² + 70w = 900
That would allow you to solve for the width (w) and then the length (2w + 70) as follows:
2w² + 70w - 900 = 0
Divide both sides by 2:
w² + 35w - 450 = 0
Factor:
(w + 45)(w - 10) = 0
That leads to two possible answers:
w = -45 or w = 10
We can't have a negative dimension so ignore the negative result. Calculate the length:
2w + 70
= 2(10) + 70
= 90
Answer:
The rectangle is 10 ft. by 90 ft.
The rectangle must have the same area.
Let w be the width (in feet)
Let 2w + 70 be the length (in feet)
The area is:
w(2w + 70) = 900
You could also expand that to:
2w² + 70w = 900
That would allow you to solve for the width (w) and then the length (2w + 70) as follows:
2w² + 70w - 900 = 0
Divide both sides by 2:
w² + 35w - 450 = 0
Factor:
(w + 45)(w - 10) = 0
That leads to two possible answers:
w = -45 or w = 10
We can't have a negative dimension so ignore the negative result. Calculate the length:
2w + 70
= 2(10) + 70
= 90
Answer:
The rectangle is 10 ft. by 90 ft.
收錄日期: 2021-04-24 08:05:58
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