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grin007 [14]
3 years ago
13

The length of a rectangular flower bed is 2ft longer than the width. If the area is 6ft, then what are the exact length and widt

h? Also find the approximate dimensions of the rectangle.
Mathematics
1 answer:
Marizza181 [45]3 years ago
7 0

Answer:

Exact dimensions:

width=-1+\sqrt{7}

length=-1+\sqrt{7}+2

length=1+\sqrt{7}

Approximate dimensions:

width=1.64575ft

length=1.64575+2

length=3.64575ft

Step-by-step explanation:

Let's assume width of rectangle is w ft

The length of a rectangular flower bed is 2ft longer than the width

so,

length =w+2

L=w+2

now, we can find area

A=L\times W

now, we can plug it

A=(w+2)\times w

A=w^2+2w

we are given area =6

so, we can set it equal

and then we can solve for w

w^2+2w=6

w^2+2w-6=0

we can use quadratic formula

ax^2+bx+c=0

x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

now, we can compare and find a,b and c

a=1 , b=2 , c=-6

w=\frac{-2\pm \sqrt{2^2-4\cdot \:1\left(-6\right)}}{2\cdot \:1}

w=-1+\sqrt{7},\:w=-1-\sqrt{7}

we know that dimension can never be negative

so, we will only consider positive value

Exact dimensions:

width=-1+\sqrt{7}

length=-1+\sqrt{7}+2

length=1+\sqrt{7}

Approximate dimensions:

width=1.64575ft

length=1.64575+2

length=3.64575ft

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