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) listen 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) listen 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 the 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: $3l^{2}-18l + 4l-24=0$, which is $3l(l - 6)+4(l - 6)=0$, or $(3l + 4)(l - 6)=0$. So $l=6$ or $l=-\frac{4}{3}$. Since length cannot be negative, $l = 6$. Then $w=3l-14=3\times6 - 14 = 4$.

Step1: Express length in terms of width

Let the width of the rectangle be $w$. The length $l$ is given by $l = 2w+3$.

Step2: Substitute into area formula

The area formula is $A=l\times w$. Substitute $l = 2w + 3$ into it: $A=(2w + 3)w=2w^{2}+3w$.

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