The length of a picture frame is 3 in. greater than the width. The perimeter is less than 52 in. How do you find the dimensions of the frame?

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The length of a picture frame is 3 in. greater than the width. The perimeter is less than 52 in. How do you find the dimensions of the frame?

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Answer 1 · 2016-12-27T00:19:37

We can at once replace $L = W + 3$ $L=W+3$

Explanation:

$P = 2 \times L + 2 \times W = 2 \times (W + 3) + 2 \times W$ $P=2xxL+2xxW=2xx(W+3)+2xxW$
$P = 2 W + 6 + 2 W = 4 W + 6$ $P=2W+6+2W=4W+6$

Now since $P < 52$ $P<52$ , we get:
$4 W + 6 < 52$ $4W+6<52$ subtracting 6:
$4 W < 52 \to W < 13$ $4W<52->W<13$

Conclusion:
Width is less than 13 inches
Length is less than 16 inches

Note :
There could not be just any combination of
$L < 16 and W < 13$ $L<16andW<13$ as $L = W + 3$ $L=W+3$ still holds.
(so $L = 15, W = 10$ $L=15, W=10$ is not allowed)

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The length of a picture frame is 3 in. greater than the width. The perimeter is less than 52 in. How do you find the dimensions of the frame?

1 Answer

Explanation:

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