the perimeter of a rectangle is 50 inches the length l is twice the width w. what is the area of the rectangle?? ❗️show work❗️
1 answer:
Hey. Let me help you on this one.
In order for us to solve this problem, we will need to set up an equation which we can solve later. I will also be attaching an image with the work shown in case you don't understand my explanation. Make sure to read over it since it will help you with your studies.
We know that the length is twice the width, meaning that
, with "a" standing for length, and "b" standing for width. Now that we have formed an equation for length, we can actually form an equation for perimeter.
Let's simplify the equation so it's easier and less confusing for us to solve it.
Let's divide 6 from both sides, thus eliminating all variables except for b on the right side.
"3" in 8.3 is repeating. This is very important to remember. Now, we know the width of the triangle. Let's find the length of the triangle so we can then multiply both numbers together and find the area.
"6" in 16.6 is repeating as well. It's crucial to remember as well. We know the values now, meaning that we can find the area of the rectangle.
Answer: Area of the rectangle is 138.8 (with 8 repeating).
In order for us to solve this problem, we will need to set up an equation which we can solve later. I will also be attaching an image with the work shown in case you don't understand my explanation. Make sure to read over it since it will help you with your studies.
We know that the length is twice the width, meaning that
Let's simplify the equation so it's easier and less confusing for us to solve it.
Let's divide 6 from both sides, thus eliminating all variables except for b on the right side.
"3" in 8.3 is repeating. This is very important to remember. Now, we know the width of the triangle. Let's find the length of the triangle so we can then multiply both numbers together and find the area.
"6" in 16.6 is repeating as well. It's crucial to remember as well. We know the values now, meaning that we can find the area of the rectangle.
Answer: Area of the rectangle is 138.8 (with 8 repeating).
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For the first question please find the attached diagram.
As per the diagram, P is the upstream point and Q is the downstream point. The distance between P and Q is 22.5 miles.
Let the speed of the boat in the still waters of the lake be represented by S.
Then, when the boat travels upstream, the net speed of the boat will be (S-6) miles per hour because the river flows downstream and thus the speed of the boat will have to be subtracted from the speed of the river.
Now, we know that the relationship between the net speed, distance and time of travel is give as:
Distance = Net Speed x Time of travel
For the upstream ride of the board we know that Distance is 22.5 miles and Net Speed is (S-6). Therefore, the above equation will become:
where
represents the time taken to travel upstream.
We can rearrange the above equation to be:
......................(Equation 1)
By similar arguments we know that the downstream speed of the boat is S+6 and the distance travelled is the same and so the time taken to travel downstream (represented by ) will be:
................(Equation 2)
Now, we know that the total time of travel should be 9 hours.
This means that: ............(Equation 3)
Plugging in the values of and
from (Equation 1) and (Equation 2) into (Equation 3), we get:
Simplifying the above we will get a quadratic equation:
The roots of this quadratic equation are:
and
Since, speed cannot be negative, is out of consideration.
The speed of the boat in the lake is thus miles per hour.
But we have a problem with S=6 too. The problem is that if S=6, then the boat will not be able to move upstream.
Let us solve problem 2
We are given that:
We can rewrite it as:
Now, the numerator can be simplified as:
Thus, our final simplified answer is:
The restriction on the variable x is that it cannot be equal to either +3 or -3 as that would make the denominator of the original question equal to zero.
Thus, the restriction is
