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3 years ago

In the figure, BCND is a rectangle and CGNR is a rhombus. The area of BCND is 90 and BC = 10. What is 3GR?

Mathematics

1 answer:

PIT_PIT [208]3 years ago

6 0

Answer:

$3GR=27$

Step-by-step explanation:

<u>Since area of rectangle BCND is given as 90 and one of its side is 10, the other side MUST be 9.</u>

In Rhombus CGNR, CN and GR are congruent (property of Rhombus). Hence GR = 9 as well.

Thus 3GR = 3(9) = 27

First answer choice is right.

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Pachacha [2.7K]

Answer:

a = 9.849

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Step-by-step explanation:

By using Pythagoras theorem in the right triangle BDC,

(Hypotenuse)² = (Leg 1)² + (Leg 2)²

BC² = BD² + DC²

a² = 9² + 4²

a = $\sqrt{(81+16)}$

a = $\sqrt{97}$

a = 9.8489

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By mean proportional theorem,

$\frac{\text{DC}}{\text{BD}}=\frac{\text{BD}}{\text{AD}}$

AD × DC = BD²

b × 4 = 9²

b = $\frac{81}{4}$

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BY Pythagoras theorem in ΔADB,

AB² = AD² + BD²

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3 years ago

Mr. Sawyer drove his car from his home to New York at the rate of 45 mph and returned over the same road at the rate of 40 mph.

AveGali [126]

Answer: Time taken by him in going = 8 hours

Time taken by him in returning = 9 hours

Step-by-step explanation:

Let the total distance from home to New York is x miles,

$\text{ Since, Time} = \frac{\text{Distance}}{\text{Speed}}$

Also, he drove his car from his home to New York at the rate of 45 mph,

⇒ $\text{ Time taken by him in going } = \frac{x}{45}\text{ hours}$

And, returned over the same road at the rate of 40 mph.

⇒ $\text{ Time taken by him in returning } = \frac{x}{40}\text{ hours}$

According to the question,

Time taken by him in returning - Time taken by him in going = 30 minutes = 1/2 hours, ( 1 hours = 60 minutes )

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Hence, the total distance from home to New York = x miles = 360 miles

⇒ $\text{ Time taken by him in going } = \frac{x}{45}\text{ hours}$

$=\frac{360}{45}=8\text{ hours}$

⇒ $\text{ Time taken by him in returning } = \frac{x}{40}\text{ hours}$

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Answer:

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Step-by-step explanation:

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