SOLUTION: The width of a rectangle is 5 cm less than half it length. Its area is 72 cm squared. Find the length and the width of the rectangle

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Question 892645: The width of a rectangle is 5 cm less than half it length. Its area is 72 cm squared. Find the length and the width of the rectangle
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
w=-5%2B2L and wL=72.

%282L-5%29L=72
2L%5E2-5L-72=0

L=%285%2B-+sqrt%2825%2B4%2A2%2A72%29%29%2F4
L=%285%2B-+sqrt%281800%29%29%2F4
L=%285%2B-+10sqrt%282%2A3%2A3%29%29%2F4
L=%285%2B-+30sqrt%282%29%29%2F4, choose the PLUS form.
highlight%28L=%285%2B30sqrt%282%29%29%2F4%29

Just use the earlier described formula for w to find its value from L.
You can use either initially described formulas, including wL=72 if you want.
w=72%2FL. If do that,
w=72%2F%28%285%2B30sqrt%282%29%29%2F4%29
w=%2872%2A4%29%2F%285%2B30sqrt%282%29%29, and should rationalize the denominator.
w=%2872%2A4%285-30sqrt%282%29%29%29%2F%2825-900%2A2%29
w=%2872%2A4%2830sqrt%282%29-5%29%29%2F%281800-25%29
w=%2872%2A4%2A5%286sqrt%282%29-1%29%29%2F1775
w=%2872%2A4%286sqrt%282%29-1%29%29%2F355
highlight%28w=%28288%2F355%29%286sqrt%282%29-1%29%29----maybe the linear form would have been easier. Should have used 2L-5 instead.

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

The width of a rectangle is 5 cm less than half it length. Its area is 72 cm squared. Find the length and the width of the rectangle


Length: highlight_green%2818%29 cm

Width:   highlight_green%284%29 cm 

You can do the check!! 



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