Question

The area of a rectangle is 300 square centimeters. If the sides of the rectangle are given as 5 centimeters and //tex.z-dn.net/?f=%20%5Csqrt%7Bx%2B2600%7D%20" id="TexFormula1" title=" \sqrt{x+2600} " alt=" \sqrt{x+2600} " align="absmiddle" class="latex-formula"> centimeters, then find the value of x and the other side of the rectangle.

Answer 1

x is 1000, and the other side of the rectangle is 60 cm.
Area is found by multiplying length by width.  Using the sides we know we have
$300=5(\sqrt{x+2600})$
We divide both sides by 5:
$\frac{300}{5}=\frac{5\sqrt{x+2600}}{5} \\ \\60=\sqrt{x+2600}$
To "undo" a square root, we square both sides:
$60^2=(\sqrt{x+2600})^2 \\ \\3600=x+2600$
Subtract 2600 from both sides:
3600-2600=x+2600-2600
1000=x
Now we substitute this into the side with x:
$\sqrt{x+2600}=\sqrt{1000+2600}=\sqrt{3600}=60$