Question

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

Answer 1

Answer:

$AB=22\ units$

Step-by-step 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

$AB=22\ units$