Question

answer the questions below.
(a) the perimeter of a rectangular field is 280 m.
if the length of the field is 75 m, what is its width?
width of the field: \boxed{} m
(b) the area of a rectangular painting is 3604 cm².
if the width of the painting is 53 cm, what is its length?
length of the painting: \boxed{} cm

Explanation:

Part (a)

Step1: Recall perimeter formula for rectangle

The formula for the perimeter \( P \) of a rectangle is \( P = 2\times (l + w) \), where \( l \) is the length and \( w \) is the width. We know \( P = 280 \) m and \( l = 75 \) m. Substitute these values into the formula: \( 280 = 2\times(75 + w) \).

Step2: Solve for \( w \)

First, divide both sides of the equation by 2: \( \frac{280}{2}=75 + w \), which simplifies to \( 140 = 75 + w \). Then, subtract 75 from both sides: \( w = 140 - 75 = 65 \).

Step1: Recall area formula for rectangle

The formula for the area \( A \) of a rectangle is \( A = l\times w \), where \( l \) is the length and \( w \) is the width. We know \( A = 3604 \) \( \text{cm}^2 \) and \( w = 53 \) cm. Substitute these values into the formula: \( 3604 = l\times53 \).

Step2: Solve for \( l \)

To find \( l \), divide both sides of the equation by 53: \( l=\frac{3604}{53}=68 \).

Answer:

65

Part (b)