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Sagot :
Dimensions of a rectangle
Writing an expression for the dimensions
Let's call each dimension by a letter:
W: width
L: length
We have that the length is 2 times the width.
This means that the length is equal to 2 times the width:
L = 2W
Area of a rectangle: equation for the unkowns
We have that the area of a rectangle is given by the product of the width and the length:
area = W · L
Since L = 2W, then:
area = W · L
↓ replacing L by 2W
area = W · 2W
area = 2W²
Since area = 65, then
65 = 2W²
Now, we have an equation that we can use to find the value of W.
Finding each dimension
Width
Using the previous equation, we can find the value for the width W:
65 = 2W²
↓ taking 2 to the left side
65/2 = W²
↓ square root of both sides
√(65/2) = √W² = W
Then,
[tex]W=\sqrt[]{\frac{65}{2}}=\frac{\sqrt[]{65}}{\sqrt[]{2}}[/tex]We have an expression for the width now, we are going to find a better expression:
[tex]\begin{gathered} W=\frac{\sqrt[]{65}}{\sqrt[]{2}}=\frac{\sqrt[]{65}\cdot\sqrt[]{2}}{\sqrt[]{2}\cdot\sqrt[]{2}} \\ =\frac{\sqrt[]{65\cdot2}}{\sqrt[]{2}^2}=\frac{\sqrt[]{130}}{2} \end{gathered}[/tex]Then, we can say that:
[tex]W=\frac{\sqrt[]{130}}{2}[/tex]Length
Since the length is 2 times W:
[tex]\begin{gathered} L=2W=2\cdot\frac{\sqrt[]{130}}{2} \\ L=\sqrt[]{130} \end{gathered}[/tex]Answer
We have that the measures for the width, W, and length, L, are:
[tex]W=\frac{\sqrt[]{130}}{2}\text{ and }L=\sqrt[]{130}[/tex]
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