Question

Rashad is considering two designs for a garden. In Design 1 he would use fencing to surround a square plot of land that has an area of 1,296 square feet. In Design 2 he would divide a plot of land into two rectangular sections, each 15 feet by 36 feet, and surround the plot with fencing, as well as place fencing along the dividing line of the two sections.

Which plan would cost less in fencing? Explain.

Design 1, because it requires 12 fewer feet of fencing than Design 2
Design 1, because it requires 24 fewer feet of fencing than Design 2
Design 2, because it requires 12 fewer feet of fencing than Design 1
Design 2, because it requires 24 fewer feet of fencing than Design 1

Answer 1

Answer:

B. Design 1 would cost less because it requires 24 fewer feet of fencing than Design 2.

Step-by-step explanation:

We are required to find the plan which would cost less in fencing.

Design 1: A square having area 1296 square feet.

Area of the square = $Side^2$

i.e. $1296=a^2$

i.e. a= 36 feet.

So, perimeter of the square = $4a$

i.e. Perimeter of the square = 4 × 36 = 144 feet.

Design 2: Two rectangles with dimensions 15 × 36 feet each.

Here, the fencing is around the plot as well as along the line dividing the land.

That is, the fencing is applied at 4 sides of length 15 feet and 3 sides of length 36 feet,

So, Perimeter of the land= 15 × 4 + 36 × 3

i.e. Perimeter of the land= 60 + 108

i.e. Perimeter of the land = 168 feet.

Thus, the difference between the perimeters = 168 - 144 = 24 feet.

Hence, we get,

Design 1 would cost less because it requires 24 fewer feet of fencing than Design 2.

Answer 2

Design 1 would cost less in fencing because it requires 24 fewer feet of fencing than design 2.

Area of the square plot = 1296 square feet

Side of the square plot = √1296 =36 square feet

What is the perimeter of a square with side a?

The perimeter of a square with side a is a².

So according to design 1, total fencing needed = 36*4 =144 feet

According to design 2, total fencing needed = fencing of two plots with dimensions of 15 feet by 36 feet each - fencing along dividing lines

Fencing needed for one rectangular plot=(15+36)*2 =102 feet

Fencing needed for two rectangular plot=204 feet

Since we are adding the fencing of the dividing line twice so we need to subtract the fencing of the dividing line.

According to design 2, total fencing needed = 204-36 = 168 feet

So, difference between design 1 and design 2 = 168-144 =24 feet

Hence, design 1 would cost less in fencing because it requires 24 fewer feet of fencing than design 2.

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