Question

4.

Answer 1

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:

$2x^2+2x+4x+4=130\\2x^2+6x+4=130$

Divide through by 2

$x^2+3x+2=65\\x^2+3x=65-2\\x^2+3x = 63$

Complete the square by adding the square of the half of the coefficient of x to both sides:

$(x^2+3x+(\frac{3}{2} )^2)=63+(\frac{3}{2} )^2$

$(x+\frac{3}{2} )^2=63 + \frac{9}{4} \\(x+\frac{3}{2} )^2=\frac{252+9}{4} \\(x+\frac{3}{2} )^2=\frac{261}{4}\\(x+\frac{3}{2} )^2=65.25$

Take the square root of both sides

$\sqrt{(x+(\frac{3}{2} ))^2} = \sqrt{65.25}\\x+\frac{3}{2}= 8.078\\x=8.078-1.5\\x=6.58m$

Hence the value of x is 6.58m