Answer:
The value of x is: [tex]5 (\sqrt5-1)\ units[/tex]
Step-by-step explanation:
Given that:
Area of rectangle = 100 sq units
Length = (x+10) units
Width = x units
We know that area of a rectangle is given by the formula:
[tex]A = l \times w[/tex]
Where l is length of rectangle and
w is the width of rectangle
Putting the values in formula:
[tex]x(x+10) = 100\\\Rightarrow x^2+10x=100\\\text{Trying to make square on both sides by Adding 25 on both sides}:\\\Rightarrow x^2+10x+25=100+25\\\Rightarrow x^2+2 \times 5 \times x+5^2=125\\\text{Formula: } a^{2} +2 \times a \times b+ b^{2} = (a+b)^2\\\Rightarrow (x+5)^2 = 25 \times 5\\\text{Taking square root on both sides:}\\\Rightarrow (x+5) = 5\sqrt5\\\Rightarrow x = 5\sqrt5-5\\\Rightarrow x = 5 (\sqrt5-1)[/tex]
So, The value of x is: [tex]5 (\sqrt5-1)\ units[/tex]
