Question

1. a rectangular lawn is 14 meters by 35 meters. it would cost $5.14 per meter to install a fence around the lawn. how much would it cost to put a fence around the lawn?
2. here are three goat pastures that share common fences. the width of each pasture is x. the total length of the three pastures is 18x + 3. if the perimeter of one of the pastures is 30 yards, what is the width?
3. given the angles shown are supplementary (equal 180 degrees), find the value of x and both angles a and b.
4. the perimeter of the given rectangle is 30 cm. the width is 2x and the length is (x + 4). find the dimensions of the rectangle.

Explanation:

Step1: Calculate perimeter of lawn

$2\times14 + 2\times35=28 + 70 = 98$ (meters)

Step2: Calculate cost

$98\times5.14 = 503.72$ (dollars)

Step1: Expand equation for goat - pasture

$2x+2(6x + 1)=2x+12x + 2=14x+2$

Step2: Solve for x

$14x+2 = 30$, $14x=28$, $x = 2$

Step1: Solve for x in angle problem

$(3x + 45)+(4x-5)=180$, $7x+40 = 180$, $7x=140$, $x = 20$

Step2: Calculate angle A

$\angle A=3x + 45=3\times20 + 45=105^{\circ}$

Step3: Calculate angle B

$\angle B=4x-5=4\times20-5 = 75^{\circ}$

Step1: Set up perimeter equation for rectangle

$2(2x)+2(x + 4)=30$, $4x+2x+8 = 30$, $6x=22$, $x=\frac{11}{3}$

Step2: Calculate width

Width $=2x=2\times\frac{11}{3}=\frac{22}{3}$ (cm)

Step3: Calculate length

Length $=x + 4=\frac{11}{3}+4=\frac{11 + 12}{3}=\frac{23}{3}$ (cm)

Answer:

$503.72$