Answer:
(x+2)(2x+2) = 130
x=6.58m
Step-by-step explanation:
The shape of the whole figure is a triangle. Hence the area of the whole figure is expressed as:
Area = Length * Width
Given
Length = 2 + x + x = 2+2x
Width = 2 + x
Area = 130m²
Substitute the resultng values into the formula;
(2+2x)(2+x)= 130
(x+2)(2x+2) = 130
Expand the bracket:
[tex]2x^2+2x+4x+4=130\\2x^2+6x+4=130\\[/tex]
Divide through by 2
[tex]x^2+3x+2=65\\x^2+3x=65-2\\x^2+3x = 63[/tex]
Complete the square by adding the square of the half of the coefficient of x to both sides:
[tex](x^2+3x+(\frac{3}{2} )^2)=63+(\frac{3}{2} )^2[/tex]
[tex](x+\frac{3}{2} )^2=63 + \frac{9}{4} \\(x+\frac{3}{2} )^2=\frac{252+9}{4} \\(x+\frac{3}{2} )^2=\frac{261}{4}\\(x+\frac{3}{2} )^2=65.25[/tex]
Take the square root of both sides
[tex]\sqrt{(x+(\frac{3}{2} ))^2} = \sqrt{65.25}\\x+\frac{3}{2}= 8.078\\x=8.078-1.5\\x=6.58m[/tex]
Hence the value of x is 6.58m
