Question

(a)The perimeter of a rectangular field is 314m.
If the length of the field is 98m, what is its width?
width of the field: --- m

(b)The area of a rectangular painting is 4488cm^2.
If the width of the painting is 51cm, what is its length?
lengght of the painting : --- cm

Answer 1

(a) To find the width of the rectangular field, we can use the formula for the perimeter of a rectangle, which is given by:

\[ P = 2 \times (L + W) \]

where \( P \) is the perimeter, \( L \) is the length, and \( W \) is the width.

Given:
- \( P = 314 \) m
- \( L = 98 \) m

We can rearrange the formula to solve for the width \( W \):

\[
314 = 2 \times (98 + W)
\]

Dividing both sides by 2:

\[
157 = 98 + W
\]

Now, subtract 98 from both sides:

\[
W = 157 - 98 = 59 \text{ m}
\]

**Width of the field: 59 m**

(b) To find the length of the rectangular painting, we can use the formula for the area of a rectangle, which is:

\[ A = L \times W \]

where \( A \) is the area, \( L \) is the length, and \( W \) is the width.

Given:
- \( A = 4488 \) cm²
- \( W = 51 \) cm

We can rearrange the formula to solve for the length \( L \):

\[
4488 = L \times 51
\]

Now, divide both sides by 51:

\[
L = \frac{4488}{51}
\]

Calculating that:

\[
L = 88 \text{ cm}
\]

**Length of the painting: 88 cm**