Question

answer the questions below.

(a) the perimeter of a rectangular field is 160 m.
if the length of the field is 54 m, what is its width?
width of the field: \boxed{} m

(b) the area of a rectangular painting is 384 cm².
if the width of the painting is 16 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 \( P = 2\times (length + width) \). We know \( P = 160 \) m and \( length = 54 \) m. Let the width be \( w \). So, \( 160 = 2\times(54 + w) \).

Step 2: Solve for width

First, divide both sides of the equation by 2: \( \frac{160}{2}=54 + w \), which simplifies to \( 80 = 54 + w \). Then, subtract 54 from both sides: \( w = 80 - 54 \).

Step 1: Recall the area formula for a rectangle

The area \( A \) of a rectangle is given by \( A = length\times width \). We know \( A = 384 \) \( cm^2 \) and \( width = 16 \) cm. Let the length be \( l \). So, \( 384 = l\times16 \).

Step 2: Solve for length

Divide both sides of the equation by 16: \( l=\frac{384}{16} \).

Answer:

\( 26 \)

Part (b)