Respuesta :
The dimension of new garden is 7 meter by 8 meter
Solution:
The dimensions of a rectangular garden were 4m by 5m
Length = 4 m
Width = 5 m
Each dimension was increased by the same amount the garden then had an area of 56 square meter
Let "x" be the amount of increase
Then,
Length = 4 + x
Width = 5 + x
Also, given that,
New area = 56 square meter
The area of rectangle is given as:
[tex]Area = length \times width[/tex]
Substituting the values we get,
[tex]56 = (4+x)(5+x)\\\\56 = 20 + 4x + 5x + x^2\\\\x^2 + 9x + 20 - 56 = 0\\\\x^2 + 9x -36=0[/tex]
Let us solve the above equation by quadratic formula
[tex]\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Using the above formula,
[tex]\text{For } x^2+9x-36 \text{ we get , }[/tex]
a = 1 and b = 9 and c = -36
Substituting the values of a = 1 ; b = 9 ; c = -36 in above quadratic formula we get,
[tex]x = \frac{-9\pm \sqrt{9^2-4\cdot \:1\left(-36\right)}}{2\cdot \:1}\\\\x = \frac{-9\pm \sqrt{81+144}}{2}\\\\x = \frac{-9 \pm 15}{2}[/tex]
We get two solutions,
[tex]x = \frac{-9+15}{2} \text{ or } x = \frac{-9-15}{2}\\\\x = 3 \text{ or } x = -12[/tex]
Since dimension cannot be negative, ignore x = -12
Thus solution is x = 3
Length = 4 + x = 4 + 3 = 7
Width = 5 + x = 5 + 3 = 8
Thus dimension of new garden is 7 meter by 8 meter
