SOLUTION: The width of a rectangle is 1 less than twice its length. If the area of the rectangle is 63 cm2 , what is the length of the diagonal? The length of the diagonal is cm 13

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Question 1142230: The width of a rectangle is 1 less than twice its length. If the area of the rectangle is 63 cm2
, what is the length of the diagonal?
The length of the diagonal is cm
13.10 or13.13? Neither work
Found 2 solutions by rothauserc, josmiceli:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
let l be the length of the rectangle and w be the width
:
w = 2l - 1
:
l * (2l-1) = 63
:
2l^2 -l -63 = 0
:
Use quadratic formula
:
l = (1 + square root((-1)^2 -4 * 2 * (-63)))/(2 * 2) = 5.87
:
l = (1 - square root((-1)^2 -4 * 2 * (-63)))/(2 * 2) = -5.37
:
ignore the negative value for l
:
w = (2 * 5.87) -1 = 10.74
:
******************************************************
diagonal = square root((5.87^2) +(10.74^2)) = 12.14cm
******************************************************
:

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let length = +L+
Width = +2L+-+1+
+L%2A%28+2L+-+1+%29+=+63+ cm2
+2L%5E2+-+L+-+63+=+0+
+L+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+L+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A2%2A%28-63%29+%29%29%2F%282%2A2%29+
+L+=+%28+1+%2B-+sqrt%28+1+%2B+504+%29%29%2F4+
+L+=+%28+1+%2B+22.472+%29%2F4+
+L+=+23.472%2F4+
+L+=+5.868+
Width = +2%2A5.868+-+1+
Width = +10.736+
Let +d+ = the length of the diagonal in cm
+d%5E2+=+5.868%5E2+%2B+10.736%5E2+
+d%5E2+=+34.4334+%2B+115.2617+
+d%5E2+=+149.6951+
+d+=+12.235+ cm
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check:
+5.868%2A10.736+=+63+
+62.9988+=+63+
close enough I think
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