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