You can use variables in place of length and width of rectangle. And since length is already given in terms of width and perimeter of rectangle is also given, thus, putting those values in the formula for perimeter of rectangle will help us get the length and width of the rectangle.
- The length of the given rectangle is: 36 cm
- The width of the given rectangle is: 9 cm
How to calculate the values of items which are not known?
Most of the times, you will get some other facts or information by which the unknown values of those items can be known. For simple daily life cases, we can use variables, which are nothing but just placeholders for those unknown values. We can then operate on those variables assuming them to be actual values, thus, getting near to their original values.
How to calculate the length and width of the given rectangle?
Since the length is given in the form of width of the rectangle, thus, we can start from using variable for width of the rectangle.
Let the width of the rectangle be denoted by [tex]w[/tex] cm.
Then as the length of the given rectangle is 4 times the width, and since 4 times is denoted by multiplication of 4, thus,
Length of the rectangle = [tex]x \times 4[/tex] cm
Perimeter of rectangle = 2(length + width)
[tex]= 2 \times ( x + 4x) = 2 \times (5x) = 10x[/tex] cm
Since perimeter is 90 cm given, thus, we have both the values equal(as perimeter is same). Thus,
[tex]10x = 90\\\\\text{Subtracting 10 from both sides}\\\\\dfrac{10x}{10} = \dfrac{90}{10}\\\\x = 9[/tex]
Thus, width of the given rectangle is 9 cm.
The length of the given rectangle is 4 times width = [tex]9 \times 4[/tex] = 36 cm
Thus,
- The length of the given rectangle is: 36 cm
- The width of the given rectangle is: 9 cm
Learn more about rectangles here:
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