SOLUTION: please help me I can up with three crazy answers. Translate the following into a quadratic equation, and solve it: The length of a rectangular garden is three times its width;

Question 172398This question is from textbook
: please help me I can up with three crazy answers.
Translate the following into a quadratic equation, and solve it: The length of a rectangular garden is three times its width; if the area of the garden is 75 square meters, what are its dimensions?
also can you show me how to check the answer after solving the problem.
This question is from textbook

Found 2 solutions by jim_thompson5910, Mathtut:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since "The length of a rectangular garden is three times its width", this means that

Area:

Start with the area formula

Plug in (the given area) and

Multiply

Rearrange the equation.

Divide both sides by to isolate .

Reduce.

Take the square root of both sides (only the positive square root is considered since a negative width doesn't make sense)

So the width is 5 m and the length (which is 3 times the width) is 3*5=15 m

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Answer:

So the width is 5 m and the length is 15 m
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
ok so the we have Width W and Length L=3W....we also know that area=LW
:
3W(W)=75
:

:
this would be easy enough to solve without the quadratic formula but since you asked for it
:

since we know we cant have negative lengths
so
=15
:
checking =..and
:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=900 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 5, -5. Here's your graph:

:

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