Question

answer the questions below.
(a) the perimeter of a rectangular field is 248 m.
if the length of the field is 73 m, what is its width?
width of the field: \boxed{} m
(b) the area of a rectangular painting is 4650 cm².
if the width of the painting is 62 cm, what is its length?
length of the painting: \boxed{} cm

Explanation:

Part (a)

Step 1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times (length + width) \), or \( P = 2l + 2w \), where \( l \) is the length and \( w \) is the width. We know \( P = 248 \) m and \( l = 73 \) m, and we need to find \( w \).

Step 2: Substitute the known values into the formula and solve for \( w \)

First, divide both sides of the perimeter formula by 2: \( \frac{P}{2}=l + w \).
Substitute \( P = 248 \) and \( l = 73 \): \( \frac{248}{2}=73 + w \).
Simplify \( \frac{248}{2} = 124 \), so we have \( 124 = 73 + w \).
Subtract 73 from both sides: \( w = 124 - 73 \).
Calculate \( 124 - 73 = 51 \).

Step 1: Recall the area formula for a rectangle

The area \( A \) of a rectangle is given by \( A = length\times width \), or \( A = l\times w \), where \( l \) is the length and \( w \) is the width. We know \( A = 4650 \) \( cm^2 \) and \( w = 62 \) cm, and we need to find \( l \).

Step 2: Substitute the known values into the formula and solve for \( l \)

From \( A = l\times w \), we can solve for \( l \) by dividing both sides by \( w \): \( l=\frac{A}{w} \).
Substitute \( A = 4650 \) and \( w = 62 \): \( l=\frac{4650}{62} \).
Calculate \( \frac{4650}{62}=75 \) (since \( 62\times75 = 4650 \)).

Answer:

(a):
\( 51 \)

Part (b)