Question

The dance floor is 20 meters long. using this information to help you follow the directions below. 1.) write an equation using variables to represent the perimeter of the dance floor. 2.) solve the equation to find the dimensions of the dance floor. 3.) write an equation using variables to represent the area of the dance floor. 4.

Answer 1

The complete question is

A dance floor has a perimeter of 60 meters. The dance floor is 20 meters long. Use this information to  help you follow the directions below.

1. Write an equation using variables to represent the perimeter of the dance floor. 2. Solve the equation to find the dimensions of the dance floor. 3. Write an equation using variables to represent the area of the dance floor. 4. Solve the equation to find the area of the dance floor.

Let

L-------->  the length side of the dance floor

W-------> the width side of the dance floor

P------> Perimeter of the dance floor

A-----> area of the dance floor

we know that

the perimeter of the dance floor is

$P=2L+2W$

therefore

the answer Part 1) is

The equation to represent the perimeter of the dance floor is

$P=2L+2W$

Part 2) Solve the equation to find the dimensions of the dance floor.

In this problem we have

$L=20\ m$

$P=60\ m$

Substitute in the Perimeter formula

$60=2*20+2W\\60=40+2W\\2W=60-40\\W=20/2\\ W=10\ m$

therefore

the answer part 2) is

the dimensions of the dance floor are

the length side of the dance floor is $20\ meters$

the width side of the dance floor is $10\ meters$

Part 3) Write an equation using variables to represent the area of the dance floor

we know that

the area of the dance floor is

$A=L*W$

therefore

the answer part 3) is

The area of the dance floor is

$A=L*W$

Part 4) Solve the equation to find the area of the dance floor.

we know that

$L=20\ m\\W=10\ m$

Substitute in the formula of area

$A=20*10$

$A=200\ m^{2}$

therefore

the answer art 4) is

the area of the dance floor is $200\ m^{2}$

Answer 2

Let x be the length.
Then the perimeter is given by the formula : 2(20+x)=40+2x.
Area of the dance floor:$x\times20$