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Anna35 [415]
2 years ago
7

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]2 years ago
3 0

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

<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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The value of distance between the station and the city in terms of miles which train and car travelled at interval of 2 hours is 129.6 miles.

<h3>What is the rate of speed?</h3>

The rate of speed is the rate at which the total distance is travelled in the time taken. Rate of speed can be given as,

r=d/t

Here, (d) is the distance travelled by the object and (t) is time taken but the object to cover that distance.

The train traveled 1/3 of the distance at 30 mph and the remaining distance at 40 mph. Let <em>t</em> is the time the train has taken to travel and x is the distance it travelled. Thus,

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After two hour a car left the same station traveled the first 3 hours at 35 mph and the remaining distance at 51 mph. Let <em>t</em> is the time the car has taken to travel and x is the distance it travelled. Thus,

t+2=3+\dfrac{(x-3\times35)}{51}

As t is same, thus put the value of t in this equation,

\dfrac{x}{36}=3-2+\dfrac{(x-3\times35)}{51}\\\dfrac{x}{36}=3-2+\dfrac{(x-3\times35)}{51}\\\dfrac{x}{36}=1+\dfrac{(x-105)}{51}\\\dfrac{x}{36}=\dfrac{(51+x-105)}{51}\\51x=36x-54\times36\\51x-36x=1944\\x=\dfrac{1944}{15}\\x=129.6

Thus, the value of distance between the station and the city in terms of miles which train and car travelled at interval of 2 hours is 129.6 miles.

Learn more about the rate of speed here:

brainly.com/question/359790

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Iteru [2.4K]
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