Question

A rectangle that had the perimeter of 70 and the area of 250 has enlarged; its sides became twice as long. what is the new area and the new perimeter

Answer 1

The perimeter of the original rectangle is:
P = 2w + 2l = 70
The area of the original rectangle is:
A = w * l = 250
Then, by modifying the length of its sides we have:
Perimeter:
P '= 2 (2w) +2 (2l)
Rewriting:
P '= 2 (2w + 2l)
P '= 2P
P '= 2 (70)
P '= 140
Area:
A '= (2w) * (2l)
Rewriting:
A '= (2) * (2) (w) * (l)
A '= 4 * w * l
A '= 4 * A
A '= 4 * 250
A '= 1000
Answer:
the new area and the new perimeter are:
P '= 140
A '= 1000