Tyler has a rectangular garden that measures 10 m wide by 13 m long. He wants to increase the area to 208 m2 by increasing the width and length by the same amount. What will be the width (shorter dimension) of the new garden?
13 m wide
14 m wide
15 m wide
16 m wide
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sorry but what do you mean? c:
i think 60 something c:
brb real quick
k i am back @pinkbubbles
ok take your time
its fine. :)
The original gardens has these dimensions.
The original garden has dimensions 13 m by 10 m.
If you increase both the length and the width by x meters, what are the new length and width?
oh i know what it is 13m right ;)
Since the area of the new rectangle is length * width, we multiply x + 13 by x + 10.
The new area is 208, so we set the new area equal to 208, and we solve for x.
(x + 13)(x + 10) = 208
\(x^2 + 10x + 13x + 130 = 208\)
\(x^2 + 23x - 78 = 0\)
\((x - 3)(x + 26) = 0\)
\(x - 3 = 0\) or \(x + 26 = 0\)
\(x = 3 \) or \(x = -26\)
Since the increase in length and width cannot be -26 m, it must be 3 m.
The original width was 10 m.
10 m + 3 m = 13 m
The new width is 13 m.
The width became 13 m, and the length became 13 m + 3 m = 16 m
\((13 ~m)(16 ~m) = 208 ~m^2\)
13 m is correct.