Answer:
Joseph is buying tomato seed packets and cucumber seed packets at the store. He plans to buy 7 seed packets of EACH type of plan
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Let as described in the problem statement. Plugging in
and
gives us the equations
and
Since
are nonzero, we divide the second equation by the first to get
which means that
after taking the cube root. Plugging this value for
into the first equation, we now have
Solving gives
and our desired exponential equation is
If the ratio of the dimensions is 4:7 and the shorter dimension is 10ft, we know that the 10ft corresponds to the 4 in this scenario. We can set up the equation as follows:
You have to multiply by 2.5 to get from 4 to 10. And since we want to make sure we are maintaining the ratio, we have to multiply the denominator, 7, by 2.5 as well.
This means your shorter side has a length of 10ft and your longer side has a length of 17.5ft.
AREA
The formula for the area of a rectangle is:
So we can plug our dimensions into the formula:
So 175 is our area. But we can't forget about units! Since this is area and we multiplied our units together, our units would be squared. That means our answer is <u>175 square feet</u>.
PERIMETER
The formula for the perimeter of a rectangle is:
We can plug our dimensions into the formula:
So 55 is our perimeter. Of course, we can't forget about our units. Because this is perimeter, we only added our units together, so they don't change. That means our answer is <u>55 feet</u>.