Question

A rectangle has a length 2 cm larger than its width.

(a) If the perimeter of the rectangle is 14 cm, what are the dimensions of the reciangle?
(b) If the area of the rectangle is 63 cmwhat are the dimensions of the rectangle?
(a) The width of the rectangle is cm, and the length of the rectangle is cm.
(Type an integer or a decimal)
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Answer 1

a) L-W=2
2L+2W=14 (perimeter)
L=W+2
2(W+2)+2W=14
2W+4+2W=14 (like terms)
4W+4=14
4W=14-4=10
W=10/4
W=2.5
and then from L=2+W
L=4.5
b) L-W=2
LW=63
L=2+W
(2+W)+W=63
2W+W^2=63
W^2+2W-63=0 (factorize)
(W-7)(W+9)=0
and then we solve separately
W-7=0
W=7
W+9=0
W=-9 (ignored because no length is negative)
W=7 L=7+2=9