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melamori03 [73]
3 years ago
6

. Shanice is making a garden. The area of the garden is 24 ft2. Use the following shape and information to find the base (6−4) a

nd height (+3) of the garden. The equation for area of a triangle is =1/2ℎ.
Mathematics
1 answer:
crimeas [40]3 years ago
3 0

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, <em>A</em> = 24 ft².

The base height of the garden are:

base (<em>b</em>) = 6x - 4

height (<em>h</em>) = x + 3

Compute the value of <em>x</em> as follows:

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\\

The last equation is a quadratic equation.

Compute the roots of the quadratic equation as follows:

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

The value of base and height are:

\text{base}=6x-4=(6\times 1.60)-4=5.60\ \text{ft}\\\\\text{height}=x+3=1.60+3=4.60\ \text{ft}

Thus, the base and height  of the garden are 4.60 ft and 5.60 ft.

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