SOLUTION: A rectangular garden has an area of 10 square feet. Four less than the width is equal to 23 less than twice the length. a) Define variables b) Write an equation, in standard

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Question 890221: A rectangular garden has an area of 10 square feet. Four less than the width is equal to 23 less than twice the length.
a) Define variables
b) Write an equation, in standard form, that models the situation.
c) Solve your quadratic equation to find the length and the width.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
w for width and L for length:
-4+w=-23+2L from the second sentence description.
That gives w-2L=4-23,
w-2L=-19
2L-w=19.

Area description means wL=10.
Choose either w or L and substitute for it in the area equation. Maybe w is most convenient to use. w=2L-19.
highlight%28%282L-19%29L=10%29, when substituted.

Standard form for the equation is not really the best way to go. Just try simplifying, and if possible, factoring.

highlight%282L%5E2-19L-10=0%29, general form.
Discriminant? 19^2-4*2(-10)=19^2+80=441=21^2.
Directly using general solution of a quadratic equation and the values from the equation,
L=%2819%2B-+21%29%2F4 MUST be only highlight%28L=%2819%2B21%29%2F4=10%29.

Use this in formula for w to find w.