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2 answers:
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The second garden plot will require 8√5 feet more fence than the first garden plot.
Further explanation:
In order to find the fence, we have to find the perimeter of both squares
So,
Area of Square 1: A1=180 square feet
Area of Square 2: A2=320 Square feet
Let x be the side of square 1:
Then,
For second square:
Let y be the side of second square
Perimeter of First Square:
Perimeter of Second Square:
The smaller perimeter will be subtracted from larger perimeter to find that how much more fence will be needed.
The second garden plot will require 8√5 feet more fence than the first garden plot.
Keywords: Radicals, Operations on Radicals
Learn more about radicals at:
#LearnwithBrainly
Part (i)
<h3>Answer: x^2 + 5x + 6</h3>-----------------
Work Shown:
(x+3)(x+2)
y(x+2) ..... Let y = x+3
y*x + y*2 ... distribute
x(y) + 2(y)
x(x+3) + 2(x+3) .... plug in y = x+3
x*x + x*3 + 2*x + 2*3 ... distribute
x^2 + 3x + 2x + 6
x^2 + 5x + 6
=====================================================
Part (ii)
<h3>Answer: 4x^2 - 16x + 7</h3>-----------------
Work Shown:
We could follow the same set of steps as shown back in part (i), but I'll show a different approach. Feel free to use the method I used back in part (i) if the visual approach doesn't make sense.
The diagram below is a visual way to organize all the terms. Many textbooks refer to it as "the box method" which helps multiply out any two algebraic expressions.
Each inner cell is found by multiplying the corresponding outer terms. For instance, in the upper left corner we have 2x*2x = 4x^2. The other cells are filled out the same way.
The terms in those four inner cells (gray boxes) are:
- 4x^2
- -14x
- -2x
- 7
The like terms here are -14x and -2x which combine to -16x, since -14+(-2) = -16.
We end up with the answer 4x^2-16x+7
