the length of a rectangle is twice of its width and its area is equal to the area of a square with 12 cm sides what will be the perimeter of the recta
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HESI A2

HESI A2 Quizlet Math

1. The length of a rectangle is twice its width, and its area is equal to the area of a square with 12 cm sides. What will be the perimeter of the rectangle to the nearest whole number?

Correct answer: A

Rationale: Let the width of the rectangle be x cm, and its length be 2x cm. The area of the rectangle is 2x * x = 2x², and the area of the square is 12² = 144 cm². Setting the areas equal gives 2x² = 144. Solving for x gives x = 6. Thus, the width is 6 cm, and the length is 12 cm. The perimeter is 2(6 + 12) = 36 cm. Therefore, the correct answer is 36 cm. Choice B, 46 cm, is incorrect because it does not match the calculated perimeter. Choices C and D are also incorrect as they do not reflect the correct calculation of the rectangle's perimeter.

2. How many pounds are in 128 ounces?

Correct answer: D

Rationale: The correct answer is D, 8 pounds. There are 16 ounces in a pound. To convert 128 ounces to pounds, you divide 128 by 16, which equals 8 pounds. Choice A, 16 pounds, is incorrect because that would be the conversion the other way around, from pounds to ounces. Choices B and C are incorrect as they do not reflect the correct conversion from ounces to pounds.

3. Solve for x: 2x - 7 = 9.

Correct answer: C

Rationale: To solve the equation 2x - 7 = 9, first, add 7 to both sides to isolate the variable: 2x = 16. Then, divide by 2 to solve for x: x = 8. Choice A (x = 10) is incorrect because the solution is x = 8, not 10. Choice B (x = 7) is incorrect as it does not correctly solve the equation. Choice D (x = 5) is incorrect as it does not yield the correct solution for x.

4. If he left a tip of $36 on a total bill of $200, what percentage of the total bill did he leave as a tip?

Correct answer: B

Rationale: To determine the tip percentage left, divide the tip amount ($36) by the total bill amount ($200), then multiply the result by 100 to express it as a percentage: (36/200) x 100 = 18%. Therefore, he left an 18% tip on the total bill amount. Choice A (16%) is incorrect because the correct calculation results in 18%. Choice C (20%) and Choice D (22%) are incorrect as they do not match the calculated percentage based on the provided numbers.

5. A pizza has a diameter of 40cm. What is its perimeter (circumference)?

Correct answer: C

Rationale: Rationale: The correct answer is obtained by applying the formula for the circumference of a circle, which is \(C = \pi \times d\), where \(d\) is the diameter of the circle. By substituting the given diameter of 40cm into the formula and performing the calculation, we find that the circumference of the pizza is 125.6cm.

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