(i)
ib)
(c)
The ratio of length and breadth of a rectangle is 4:3. If its breadth is 12 m find:
Length of the
rectangle
(1)
(i)
Perimeter of the rectangle.
(ii) Area of the rectangle
The ratio of length and breadth of a rectangle is 9:7. If its length is 18 m find:
(ii) Area of the rectangle
(i)
Breadth of the rectangle
(ii) Perimeter of the rectangle.

A ratio in mathematics, such as 4:3, represents a relationship between two numbers showing how much one value contains or is contained within another. In the example 4:3, it means that for every 4 units of length, there are 3 units of breadth. Ratios are used to compare quantities or sizes.

Solution

1)

We need to find the length. Let the length be x and breadth be y

[tex]\frac{x}{y} = \frac{4}{3}[/tex]

[tex]\frac{x}{12cm} = \frac{4}{3}[/tex]

Cross-multiply

[tex]3x = 48cm[/tex]

Divide both sides by the coefficient of x

[tex]\frac{3x}{3} = \frac{48cm}{3}[/tex]

[tex]\bold{x = 16cm}[/tex]

2)

[tex]\frac{18m}{y} = \frac{9}{7}[/tex]

Cross-multiply

[tex]9y = 126m[/tex]

Divide both sides by the coefficient of y

[tex]\frac{9y}{9} = \frac{126m}{9}[/tex]

[tex]\bold{y = 14m}[/tex]

The perimeter of the rectangle

Formula: P = 2(l + b)

Where:

P represents the perimeter
l means length
b means breadth

1 i)

P = 2(l + w)

P = 2(16cm + 12cm)

P = 2(28cm)

P = 56 cm

2 ii)

P = 2(l + b)

P = 2(18m + 14m)

P = 2(32m)

P = 64m

Area of the rectangle

Formula: A = l * b

Where:

A represents the area
l is the length
b is the breadth of the rectangle.

1 ii)

A = l * b

A = 16cm * 12cm

A = 192cm^2 | [tex]192\text{ cm}^2[/tex]

2 ii)

A = l * b

A = 18m * 14m

A = 252m^2 | [tex]252\text{ m}^2[/tex]