Answer :
The current area is 15 x 9 = 135 square feet.
He wants to increase both the length and width by X:
Set up an equation:
(15 +x) * (9 +x) = 135 * 2
Simplify :
x^2 + 24x + 135 = 270
Subtract 270 from both sides:
x^2 + 24x - 135 = 0
Use the quadratic formula to solve for x:
-24 +/- √(24^2 - 4(1*-135) / 2*1
x = 4.7 or -28.7
The answer has to be a positive value, so x = 4.7 feet.
The length and width of the rectangular shaped vegetable garden will be increased in 4.7 ft
Quadrilaterals
There are different types of quadrilaterals, for example: square, rectangle, rhombus, trapezoid and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.
The area of rectangles can be found from the equation:
A=length(l) x height (h).
Thus, initial area is Ao=lh= 15*9=135 ft².
After that, you should convert the information given in the title of the question in an algebraic expression. Hence,
(15+x)*(9+x)=2Ao
(15+x)*(9+x)=2*135
135+15x+9x+x²=270
x²+24x-135=0
Solving the quadratic formula.
[tex]x_{1,\:2}=\frac{-24\pm \sqrt{24^2-4\cdot \:1\cdot \left(-135\right)}}{2\cdot \:1}[/tex]
[tex]x_{1,\:2}=\frac{-24\pm \:6\sqrt{31}}{2\cdot \:1}=-12\pm \:3\sqrt{31}}[/tex]
Thus, [tex]x_{1}=-12+3\sqrt{31}}=4.7[/tex] and [tex]x_{2}=-12-3\sqrt{31}}=-28.7[/tex]. The value of x is equal to 4.7 ft since x must be positive number.
Read more about the area of rectangle here:
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