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What is the new perimeter of a rectangle that once was 13 cm by 11 cm but now having its dimensions reduced by equal amounts its area is now 111.36 square cm showing work from start to finish?
Wiki User
∙ 7y ago
Let its new length and width be 13-x and 11-x:-
If: (13-x)(11-x) = 111.36
Then: 143-24x+x^2 = 111.36
So: 143-24x+x^2 -111.36 = 0 => 31.64-24x+x^2 = 0
Using the quadratic equation formula: x = 1.4 or x = 22.6
Therefore: x = 1.4 and it can't be 22.6 because it would have negative dimensions
New dimensions: 13-1.4 = 11.6 length and 11-1.4 = 9.6 width
New perimeter: 2(11.6+9.6) = 42.4 cm
Check: 11.6*9.6 = 111.36 square cm
Wiki User
∙ 7y ago
Wiki User
∙ 7y agoThe original sides are 13 and 11. That is length - width = 2.Suppose the new width = x cm
then the new length is x + 2 cm
Therefore area = x*(x + 2)
So x*(x + 2) = 111.36
x^2 + 2x = 111.36
x^2 + 2x + 1 = 112.36
(x + 1)^2 = 112.36
(x + 1) = +/- 10.6
Since x is the measure of a side, x > 0,
therefore x = -1 + 10.6 = 9.6
and then length = x 2 = 11.6
Thus, the new dimensions are 9.6 cm * 11.6 cm.
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