A piece of land is to be fenced and subdivided as shown so that each rectangle has the same dimensions. Express the total amount of fencing needed as an algebraic expression in x.

If two or more rectangles have the same dimensions is because they are congruent. In this way, they share two corresponding sides. Our first rectangle has the following sides:

L1 = x

L2 = 3x + 4

Therefore the second and third rectangles need to have the same sides. Therefore, we will have that the sides of the second one is also:

L1 = x

L2 = 3x + 4

and the sides of the third one is also:

L1 = x

L2 = 3x + 4

Therefore, the total amount of fencing needed is:

T = 3(3x + 4) + 4(x)

T = 9x + 12 + 4x

T = 13x + 12

Moreover, we can compute the area of the fence as follows:

A = [(3x + 4) + (3x + 4) + (3x + 4)]x = (3x + 3x + 3x + 4 + 4 + 4)x

A = (9x + 12)x

A = 9x² + 12x

francocanacari francocanacari · Answer 2 · 2022-02-21T13:51:45+01:00

The algebraic expression that expresses the total amount of fencing needed is 11X + 20.

Calculus

Given that a piece of land is to be fenced and subdivided as shown so that each rectangle has the same dimensions, to express the total amount of fencing needed as an algebraic expression in X, the following calculation must be performed:

3X + 4 = 6 wooden fence blocks
Each rectangle has 3 blocks on each side and 6 blocks in front.
Number of fronts = 3
Number of sides = 4
(3X + 4) x 3 + ((3X + 4) x 4) / 2 = Algebraic expression
9X + 12 + (4X + 16) / 2 = Algebraic expression
9X + 12 + 2X + 8 = Algebraic expression
11X + 20 = Algebraic expression

Therefore, the algebraic expression that expresses the total amount of fencing needed is 11X + 20.

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