Answer:
The base and height of the garden are 4.60 ft and 5.60 ft.
Step-by-step explanation:
The area of the garden is, A = 24 ft².
The base height of the garden are:
base (b) = 6x - 4
height (h) = x + 3
Compute the value of x as follows:
[tex]A=\frac{1}{2}\times b \times h\\\\24=\frac{1}{2}\times (6x-4) \times (x+3)\\\\48=6x^{2}+18x-4x-12\\\\6x^{2}+14x-60=0\\\\3x^{2}+7x-30=0\\[/tex]
The last equation is a quadratic equation.
Compute the roots of the quadratic equation as follows:
[tex]x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }\\x = \frac{ -14 \pm \sqrt{14^2 - 4(3)(-30)}}{ 2(3) }\\x = \frac{ -14 \pm \sqrt{556}}{ 6 }\\x = \frac{ -14 }{ 6 } \pm \frac{2\sqrt{139}\, }{ 6 }\\x = -\frac{ 7}{ 3 } \pm \frac{ \sqrt{139}\, }{ 3 }\\x = 1.59661\\x\approx 1.60[/tex]
The value of base and height are:
[tex]\text{base}=6x-4=(6\times 1.60)-4=5.60\ \text{ft}\\\\\text{height}=x+3=1.60+3=4.60\ \text{ft}[/tex]
Thus, the base and height of the garden are 4.60 ft and 5.60 ft.
