Question

The perimeter of (the distance around) ABCD is 66, and DC is twice as long as CB. How long is AB?

Answer 1

`AB=22\ units`

Explanation:

we know that

In this problem ABCD is a rectangle

so

DC=AB

BC=AD

Let

BC ---> the length of rectangle

DC ---> the width of rectangle

we know that

The perimeter of rectangle is equal to

`P=2(BC+DC)`

we have

`P=66\ units`

so

`66=2(BC+DC)`

simplify

`33=BC+DC` ----> equation A

`DC=2BC` ----> equation B

substitute equation B in equation A

`33=BC+2BC`

Solve for BC

Combine like terms

`33=3BC`

Divide by 3 both sides

`BC=11\ units`

Find the value of DC

`DC=2BC` ---->
`DC=2(11)=22\ units`

Remember that

DC=AB

therefore

`AB=22\ units`