Question

1. find the perimeter and area of a rectangle with a length of $(6x-10)$ and a width of $(4x+3)$.

perimeter: _______________
area: _______________

1. the perimeter of the triangle below is $(12x-7)$. find the length of the missing side.

$(x-8)$
$(8x+4)$

Explanation:

Step1: Recall rectangle perimeter formula

Perimeter $P = 2(\text{length} + \text{width})$

Step2: Substitute length and width

$P = 2[(6x-10)+(4x+3)]$

Step3: Simplify inside parentheses

$P = 2(10x - 7)$

Step4: Distribute the 2

$P = 20x - 14$

Step5: Recall rectangle area formula

Area $A = \text{length} \times \text{width}$

Step6: Substitute length and width

$A = (6x-10)(4x+3)$

Step7: Expand using FOIL method

$A = 6x(4x) + 6x(3) -10(4x) -10(3)$

Step8: Calculate and combine terms

$A = 24x^2 +18x -40x -30 = 24x^2 -22x -30$

Step9: Recall triangle perimeter rule

Missing side = Total perimeter - sum of known sides

Step10: Sum the known sides

$(x-8)+(8x+4) = 9x -4$

Step11: Subtract from total perimeter

$\text{Missing side} = (12x-7)-(9x-4)$

Step12: Simplify the expression

$\text{Missing side} = 12x -7 -9x +4 = 3x -3$

Answer:

1. Perimeter: $20x - 14$

Area: $24x^2 -22x -30$

1. Missing side length: $3x - 3$