Question

9. The perimeter and the ratio of the

length to the width of a rectangle are
given. Find the length and width of the
rectangle.
Perimeter: 132 cm 1:w = 7:4

Answer 1

Length: 42, width: 24

Explanation:

Perimeter: 132

L: W = 7:4

7u+7u+4u+4u= 22u (Length + length + width + width)

132/22= 6 (1u)

6x4= 24 (Width/ 4u)

6x7=42 (length/7u)

recheck:

42+42+24+24= 132cm

perimeter= 132

Answer 2

The length of the rectangle is 42 cm, and the width is 24 cm.

Let the length of the rectangle be \(7x\) and the width be \(4x\), where \(x\) is a positive constant. The given information is that the ratio of the length to the width is \(7:4\).

The perimeter of a rectangle is given by \(P = 2l + 2w\), where \(l\) is the length and \(w\) is the width.

\[ P = 2(7x) + 2(4x) \]

\[ 132 = 14x + 8x \]

\[ 22x = 132 \]

\[ x = 6 \]

Now that we have the value of \(x\), we can find the length and width:

Length (\(l\)) = \(7x = 7 \times 6 = 42\) cm

Width (\(w\)) = \(4x = 4 \times 6 = 24\) cm

Therefore, the length of the rectangle is 42 cm, and the width is 24 cm.