Question

the width of a rectangle is 14 feet less than 3 times the length. if the area is 24 ft², find the width and length.
width = 10 and length = 12
width = 2 and length = 4
width = 4 and length = 6
width = 6 and length = 8
question 30 (5 points)
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the length of a rectangle is 3 more than twice the width. the area of a rectangle is given by the formula a = l×w. which of the following equations could be used to find the area?
a = 2w² + 3
a = 2w² + 3w
a = 3w² + 2w
a = 2w²
question 31 (5 points)
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multiply using the foil method: (2x + 3)(x - 4)
2x² - 5x - 12
2x² + 11x - 12
2x² - 11x - 12
2x² + 5x - 12

Explanation:

Question 1

Step1: Set up equations

Let the length of the rectangle be $l$ and the width be $w$. We know that $w = 3l-14$ and $A=l\times w = 24$. Substitute $w$ into the area - formula: $l(3l - 14)=24$. Expand to get $3l^{2}-14l - 24 = 0$. Factor the quadratic equation: $3l^{2}-14l - 24=(3l + 4)(l - 6)=0$. Solving for $l$, we get $l = 6$ or $l=-\frac{4}{3}$. Since length cannot be negative, $l = 6$. Then $w=\frac{24}{l}=\frac{24}{6}=4$.

Step1: Express length in terms of width

Given that the length $l$ of a rectangle is $l = 2w+3$, and the area formula is $A=l\times w$.

Step2: Substitute length into area formula

Substitute $l = 2w + 3$ into $A=l\times w$, we get $A=(2w + 3)w=2w^{2}+3w$.

Step1: Apply FOIL method

$(2x + 3)(x - 4)=2x\times x+2x\times(-4)+3\times x+3\times(-4)$.

Step2: Simplify the expression

$2x^{2}-8x + 3x-12=2x^{2}-5x - 12$.

Answer:

Width = 4 and Length = 6

Question 2