Question

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

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

Answer 1

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

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

where \(P\) is the perimeter, \(L\) is the length, and \(W\) is the width. Given that the perimeter is 314 m and the length is 98 m, we can substitute these values into the formula:

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

Now, divide both sides by 2:

\[
157 = 98 + W
\]

Next, subtract 98 from both sides:

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

So, the width of the rectangular field is **59 m**.

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

\[
A = L \times W
\]

where \(A\) is the area, \(L\) is the length, and \(W\) is the width. Given that the area is 4488 cm² and the width is 51 cm, we can rearrange the formula to solve for length:

\[
L = \frac{A}{W}
\]

Substituting the values we have:

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

Calculating this gives:

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

So, the length of the rectangular painting is **88 cm**.