Question

Find the dimensions of a rectangle whose perimeter is 22 meters and whose area is 30 square meters

Answer 1

The dimensions of rectangle are 5 m x 6 m

Explanation:

Let

x -----> the length of rectangle

y ----> the width of rectangle

we know that

The area of a rectangle is

`A=xy`

`A=30\ m^2`

so

`30=xy` -----> equation A

The perimeter of a rectangle is

`P=2(x+y)`

`P=22\ m`

so

`22=2(x+y)`

simplify

`11=(x+y)`

isolate the variable y

`y=11-x`-----> equation B

we have

`30=xy` -----> equation A

`y=11-x`-----> equation B

Substitute equation B in equation A

`30=x(11-x)`

`30=-x^2+11x`

`x^2-11x+30=0`

Solve the quadratic equation by graphing

using a graphing tool

the solution is x= 5 or x=6

see the attached figure

Find out the value of y

For x=5

`y=11-5=6`

For x=6

`y=11-6=5`

therefore

The dimensions of rectangle are 5 m x 6 m