Answer :
Answer:
1)
Length - 16cm
The perimeter of the rectangle - 56 cm
Area of the rectangle - 192cm^2
2)
Breadth - 14m
The perimeter of the rectangle - 64 m
Area of the rectangle - 252m^2
Step-by-step explanation:
Given:
1)
- The length ratio to breadth is 4:3
- The breadth is 12 cm
2)
- The length ratio to breadth is 9:7
- The length is 18 m
What is ratio
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]
