A rectangle has side lengths of 5 centimeters and 3 centimeters. if the side lengths are doubled, will the area also doubal? Explain
No, the area of similar shapes is proportional to the square of the corresponding sides
So 2:1 ----> 2^2 : 1^2 = 4 : 1
The area would be 4 times as large, or quadrupled.
Proof:
area of original = 5*3 = 15
new sides are 10 and 6
new area = 10*6 = 60
and 60 = 4 times 15
To determine whether the area of a rectangle will double when its side lengths are doubled, we need to calculate the areas before and after doubling the side lengths.
First, let's find the area of the original rectangle with side lengths of 5 cm and 3 cm. The formula to calculate the area of a rectangle is:
Area = Length × Width
Area = 5 cm × 3 cm = 15 square cm
Now, let's double the side lengths. After doubling, the new side lengths will be 2 × 5 cm = 10 cm and 2 × 3 cm = 6 cm.
Next, we calculate the area of the rectangle with the new side lengths:
Area = Length × Width
Area = 10 cm × 6 cm = 60 square cm
Comparing the original area of 15 square cm to the new area of 60 square cm, we can see that the area has increased by a factor of 4 (60 ÷ 15 = 4).
Therefore, when the side lengths of a rectangle are doubled, the area increases by a factor of 4, not double.
To determine whether the area of a rectangle will double when its side lengths are doubled, we need to understand the relationship between the dimensions and the area of a rectangle.
The formula for calculating the area of a rectangle is given by:
Area = Length x Width
In this case, we are given that the original length of the rectangle is 5 centimeters and the original width is 3 centimeters.
So, the original area is:
Original Area = 5 cm x 3 cm = 15 cm²
Now, let's double the side lengths to find the new dimensions.
If we double the length, we get 5 cm x 2 = 10 cm.
If we double the width, we get 3 cm x 2 = 6 cm.
The new dimensions are 10 cm for the length and 6 cm for the width.
Now, let's calculate the new area using the new dimensions:
New Area = 10 cm x 6 cm = 60 cm²
As we can see, the new area is 60 cm², which is four times greater than the original area of 15 cm². Therefore, the area is quadrupled, not doubled, when the side lengths are doubled.