Find the dimensions of a rectangle whose perimeter is 46m and whose are is 126m^2. Let the width be w. Use the perimeter to find the length in terms of w.

Question

Mathematics

Joan

31 July, 01:21

Find the dimensions of a rectangle whose perimeter is 46m and whose are is 126m^2. Let the width be w. Use the perimeter to find the length in terms of w.

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Cinnamon · Answer 1

9 and 14

Step-by-step explanation:

We know that the perimeter is equal to:

P = 2l + 2w = 46

If we divide by 2, we are left with:

l + w = 23

I = 23 - w

Now the area is equal to:

A = l * w = 126

l * w = 126

Now replacing it, we are left with:

(23 - w) * (w) = 126

(-w ^ 2) + 23 * w = 126

Rearranging:

w ^ 2 + - 23 * w + 126 = 0

We factor and we have:

(w - 9) * (w - 14) = 0

w - 9 = 0 = > w = 9

w - 14 = 0 = > 2 = 14

If w = 9, l = 23 - 9 = 14

If w = 14, l = 23-14 = 9

So the dimensions are 9 and 14.