Question

1. reinforce for each shape described, write an equation to represent the situation. then solve the equation to find the missing dimension. a. a rectangle with area 51 cm² and width 3 cm b. a rectangle with area 27 in² and length 6 in. c. a rectangle with area 4 m² and length 3 m d. a parallelogram with area 60 ft² and base 15 ft.

Explanation:

Part a

Step1: Define area formula for rectangle

The area of a rectangle is $A = l \times w$, where $A$ is area, $l$ is length, $w$ is width. Substitute known values:
$51 = l \times 3$

Step2: Solve for missing length

Divide both sides by 3:
$l = \frac{51}{3}$

Step3: Calculate the value

$l = 17$

Part b

Step1: Define area formula for rectangle

Use $A = l \times w$, substitute known values:
$27 = 6 \times w$

Step2: Solve for missing width

Divide both sides by 6:
$w = \frac{27}{6}$

Step3: Simplify the fraction

$w = \frac{9}{2} = 4.5$

Part c

Step1: Define area formula for rectangle

Use $A = l \times w$, substitute known values:
$4 = 3 \times w$

Step2: Solve for missing width

Divide both sides by 3:
$w = \frac{4}{3}$

Part d

Step1: Define area formula for parallelogram

The area of a parallelogram is $A = b \times h$, where $b$ is base, $h$ is height. Substitute known values:
$60 = 15 \times h$

Step2: Solve for missing height

Divide both sides by 15:
$h = \frac{60}{15}$

Step3: Calculate the value

$h = 4$

Answer:

a. Length = 17 cm
b. Width = 4.5 in (or $\frac{9}{2}$ in)
c. Width = $\frac{4}{3}$ m
d. Height = 4 ft