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3 years ago

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

Mathematics

1 answer:

ArbitrLikvidat [17]3 years ago

3 0

Answer:

$AB=22\ units$

Step-by-step explanation:

we know that

In this problem ABCD is a rectangle

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

$P=66\ units$

$66=2(BC+DC)$

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

$BC=11\ units$

<em>Find the value of DC</em>

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

Remember that

DC=AB

therefore

$AB=22\ units$

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