What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 2.5?
a
Perimeter = 38 cm, area = 89.25 cm2
b
Perimeter = 38 cm, area = 300 cm2
c
Perimeter = 70 cm, area = 89.25 cm2
d
Perimeter = 70 cm, area = 300 cm2
Answers
d) P=70cm, area = 300cm²
Given:
The dimensions of the rectangle are 6 cm × 8 cm.
To find:
What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 2.5?
Solution:
From the given information, we have the data as follows.
The dimensions of the rectangle are 6 cm × 8 cm.
The dimensions of the rectangle are enlarged using a scale factor of 2.5.
The new dimensions of the rectangle are:
= (6 × 2.5) cm × (8 × 2.5) cm.
= (6 × 5/2) cm × (8 × 5/2) cm.
= (3 × 5) cm × (4 × 5) cm.
= 15 cm × 20 cm.
The perimeter and the area of the rectangle are given as follows.
The perimeter: P = 2(l + b)
Substitute the values in the above equation.
P = 2(15 + 20)
P = 2 (35)
P = 70 cm.
The area: A = l × b
Substitute the values in the above equation.
A = 15 × 20
A = 300 cm².
Therefore, the option d Perimeter = 70 cm, area = 300 cm² is correct.