Respuesta :
Answer:
7mX12m
Step-by-step explanation:
I found the factors of 84 and then figured out which one would equal 5 if subtracted from each other.
You can use the fact that length is expressed in terms of width so you can take it as a variable and then try to find the area. That will give you an equation which will then help to find the value of the unknown variable x.
- The length of the given rectangle is 12 meters
- The width of the given rectangle is 7 meters
How to form mathematical expression from the given description?
You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
How to find the length and width of the rectangle if they are related and the area of that rectangle is given?
Since length of the rectangle is expressed in terms of width of that rectangle, we can take the width of the rectangle to be some variable then construct the length's expression(as the reverse will be a bit tough)
Let the width of the rectangle be [tex]w[/tex] units.
Then, by the given description, length is 5 meters longer than the width, thus,
[tex]length = width + 5 = w + 5[/tex]
Since the area of a rectangle is given as
[tex]Area = length \times width[/tex]
And as area of the considered rectangle is given as 84 square inches
Thus,
[tex]84 = (x + 5) \times (x) = x^2 + 5x\\x^2 + 5x - 84 = 0[/tex]
Comparing it with the standard form of the quadratic equation [tex]ax^2 + bx + c = 0[/tex] whose solution is given as [tex]x= \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
we get
[tex]a = 1\\b = 5\\c = -84[/tex]
Thus, the solutions would be
[tex]x= \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{-5 \pm \sqrt{25 + 336}}{2} = \dfrac{-5 \pm 19}{2}[/tex]
x = 7 or x= -12
Since x is measure of a length, thus a non negative quantity, thus, it cannot be negative.
Thus, x = 7 meters = width
and length = x + 5 = 12 meters
Thus,
- The length of the given rectangle is 12 meters
- The width of the given rectangle is 7 meters
Learn more about quadratic equations here:
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