Solve for the perimeter and unknown side length of rectangles given width and length, or perimeter and one…

Question

Solve for the perimeter and unknown side length of rectangles given width and length, or perimeter and one side length.

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

:
To find the perimeter of a rectangle whose width is $40 \text{ cm}$ and length is $60 \text{ cm}$ .

Recall the formula for the perimeter of a rectangle.
The perimeter $P$ of a rectangle with length $l$ and width $w$ is given by:
$P = 2(l + w)$
Substitute the given values into the formula.
Given $l = 60 \text{ cm}$ and $w = 40 \text{ cm}$ .
$P = 2(60 \text{ cm} + 40 \text{ cm})$
Perform the addition inside the parentheses.
$P = 2(100 \text{ cm})$
Multiply to find the perimeter.
$P = 200 \text{ cm}$
The perimeter of the rectangle is $\boxed{\text{200 cm}}$ .

:
Find the value of 'L' in the figure below if the perimeter is $140 \text{ cm}$ .
The figure shows a rectangle with one side labeled 'L' and the adjacent side labeled $40 \text{ cm}$ .
Recall the formula for the perimeter of a rectangle.
The perimeter $P$ of a rectangle with length $l$ and width $w$ is given by:
$P = 2(l + w)$
Identify the given values from the problem and the figure.
Given perimeter $P = 140 \text{ cm}$ .
From the figure, one side is $L$ and the other side is $40 \text{ cm}$ . Let $l = L$ and $w = 40 \text{ cm}$ .
Substitute the known values into the perimeter formula.
$140 \text{ cm} = 2(L + 40 \text{ cm})$
Divide both sides by 2.
$\frac{140 \text{ cm}}{2} = L + 40 \text{ cm}$ $70 \text{ cm} = L + 40 \text{ cm}$
Subtract $40 \text{ cm}$ from both sides to solve for $L$ .
$70 \text{ cm} - 40 \text{ cm} = L$ $30 \text{ cm} = L$
The value of $L$ is $\boxed{\text{30 cm}}$ .

Solve for the perimeter and unknown side length of rectangles given width and length, or perimeter and one side length.