Question

distinguishing between the area and perimeter of a rectangle
24 ft
19 ft
(a) use the calculator to find the perimeter and area of the lawn.
make sure to include the correct units.
perimeter:
area:
(b) the lawn will be surrounded by a rope.
which measure would be used in finding how much rope to buy?
perimeter area
(c) the lawn will be mowed.
which measure would be used in finding how long it will take?
perimeter area

Explanation:

Step1: Calculate Perimeter of Rectangle

The formula for the perimeter of a rectangle is \( P = 2\times (l + w) \), where \( l = 24\) ft (length) and \( w = 19\) ft (width).
Substitute values: \( P = 2\times(24 + 19) = 2\times43 = 86\) ft.

Step2: Calculate Area of Rectangle

The formula for the area of a rectangle is \( A = l\times w \).
Substitute values: \( A = 24\times19 = 456\) \( \text{ft}^2 \).

Step3: Analyze Rope Requirement (Part b)

Rope surrounds the lawn, so we need the distance around the lawn, which is the perimeter.

Step4: Analyze Mowing Time (Part c)

Mowing time depends on the area to be mowed (the surface to cover), so we use the area.

Part (a)

Perimeter: \( 86 \) ft
Area: \( 456 \) \( \text{ft}^2 \)

Part (b)

The measure used is Perimeter (since rope length equals the perimeter of the lawn).

Part (c)

The measure used is Area (since mowing time depends on the area to be mowed).

Answer:

s:
(a) Perimeter: \(\boldsymbol{86}\) ft; Area: \(\boldsymbol{456}\) \(\text{ft}^2\)
(b) \(\boldsymbol{\text{Perimeter}}\)
(c) \(\boldsymbol{\text{Area}}\)