Drew has a rectangular postcard that is 6
inches long and 4 inches wide. He uses a
photocopier to enlarge it, so that the length
and width are 1.5 times as long as those
of the original postcard. Explain how the
perimeter and area change.
FOR ALL SIMILAR GEOMETRIES:
all lengths including perimeter scale with the length scale so if you multiply lengths by 1.5 then you multiply perimeter by 1.5
Area is proportional to lengths squared so multiplying lengths by 1.5 multiplies areas by 2.25
1000
To determine how the perimeter and area change when the postcard is enlarged, we need to calculate the new length and width of the enlarged postcard.
Given that the original postcard is 6 inches long and 4 inches wide, we can find the new length and width by multiplying their original values by 1.5:
New Length = 6 inches * 1.5 = 9 inches
New Width = 4 inches * 1.5 = 6 inches
Now let's calculate the perimeter of the original and enlarged postcards.
Perimeter is calculated by adding up the lengths of all sides. Therefore, the perimeter of the original postcard is:
Original Perimeter = 2 * (Length + Width)
= 2 * (6 + 4)
= 2 * 10
= 20 inches
On the other hand, the perimeter of the enlarged postcard is:
New Perimeter = 2 * (New Length + New Width)
= 2 * (9 + 6)
= 2 * 15
= 30 inches
So, the perimeter has increased from 20 inches to 30 inches.
Now let's calculate the area of the original and enlarged postcards.
Area is calculated by multiplying the length and width. Therefore, the area of the original postcard is:
Original Area = Length * Width
= 6 * 4
= 24 square inches
The area of the enlarged postcard is:
New Area = New Length * New Width
= 9 * 6
= 54 square inches
So, the area has increased from 24 square inches to 54 square inches.
In summary, when the original postcard is enlarged using the photocopier to have lengths and widths 1.5 times longer than before, the perimeter increases from 20 inches to 30 inches, and the area increases from 24 square inches to 54 square inches.