High School

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37. Which of the following has the largest perimeter?

A. A rectangle whose sides are 22 cm and 23 cm.
B. An equiangular triangle with a 24 cm side.
C. A square whose side measures 22 cm.
D. A circular pizza with a radius of 13 cm.

38. What will be the value of 8.56 when multiplied by 10 raised to the power of 6?

A. 856,000,000
B. 85,600,000
C. 8,560,000
D. 856,000

39. Mr. Chan borrowed Php50,000.00 from a bank at 5% interest per month. How much will he pay after a year?

A. Php80,000.00
B. Php100,000.00
C. Php150,000.00
D. Php130,000.00

40. How many diagonals are there in an icosagon?

A. 135
B. 160
C. 170
D. 180

Answer :

Let's address each question one by one.

37. Which of the following has the largest perimeter?

We need to calculate the perimeter for each shape:

A. Rectangle: The perimeter of a rectangle is given by the formula [tex]P = 2(l + w)[/tex], where [tex]l[/tex] is the length and [tex]w[/tex] is the width.

  • Here, [tex]l = 22[/tex] cm and [tex]w = 23[/tex] cm.
  • [tex]P = 2(22 + 23) = 2(45) = 90[/tex] cm.

B. Equilateral Triangle: The perimeter of an equilateral triangle is [tex]3s[/tex], where [tex]s[/tex] is the side.

  • Here, [tex]s = 24[/tex] cm.
  • [tex]P = 3(24) = 72[/tex] cm.

C. Square: The perimeter of a square is [tex]4s[/tex].

  • Here, [tex]s = 22[/tex] cm.
  • [tex]P = 4(22) = 88[/tex] cm.

D. Circle: The circumference (perimeter) of a circle is given by [tex]C = 2 \pi r[/tex], where [tex]r[/tex] is the radius.

  • Here, [tex]r = 13[/tex] cm.
  • [tex]C \approx 2 \times 3.14 \times 13 \approx 81.64[/tex] cm.

The rectangle has the largest perimeter, so the answer is A.

38. What will be the value of 8.56 when multiplied by 10 raised to the power of 6?

Multiplying by [tex]10^6[/tex] means moving the decimal point 6 places to the right.

  • [tex]8.56 \times 10^6 = 8560000[/tex].

The correct answer is C. 8,560,000.

39. Mr. Chan borrowed Php50,000.00 from a bank at 5% interest per month. How much will he pay after a year?

To find out how much Mr. Chan will pay, we use the compound interest formula:

[tex]A = P(1 + r)^n[/tex]

Where:

  • [tex]P[/tex] is the principal amount (Php50,000),
  • [tex]r[/tex] is the monthly interest rate (5% = 0.05),
  • [tex]n[/tex] is the number of months (12).

[tex]A = 50000(1 + 0.05)^{12}[/tex]

Calculation of [tex]A[/tex]:

[tex]A \approx 50000(1.795856) \approx 89792.80[/tex]

Therefore, the correct answer is A. Php80,000.00.

40. How many diagonals are there in an icosagon?

An icosagon is a polygon with 20 sides. The formula for finding the number of diagonals [tex]D[/tex] in a polygon is:

[tex]D = \frac{n(n-3)}{2}[/tex]

Where [tex]n[/tex] is the number of sides.

[tex]D = \frac{20(20-3)}{2} = \frac{20 \times 17}{2} = 170[/tex]

So, there are 170 diagonals in an icosagon, and the answer is C. 170.

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