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The perimeter of the equilateral triangle below is 36cm. Find the value of e.

Mathematics

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: Speed Calculation

  1. Convert the given time to a decimal or improper fraction.

    Given time = 2122\frac{1}{2} hours = 2.5 hours.
    Given distance = 120 km.

  2. Use the formula for speed.

    Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}} Speed=120 km2.5 hours\text{Speed} = \frac{120 \text{ km}}{2.5 \text{ hours}} Speed=48 km/h\text{Speed} = 48 \text{ km/h}

    The speed at which the bus was travelling is 48 km/h\boxed{\text{48 km/h}}.

    : Probability

  3. Recall the relationship between the probability of an event happening and not happening.

    The sum of the probability of an event happening and the probability of it not happening is 1.

    P(winning)+P(losing)=1P(\text{winning}) + P(\text{losing}) = 1

    Given P(winning)=37P(\text{winning}) = \frac{3}{7}.

  4. Calculate the probability of Benon losing the game.

    P(losing)=1−P(winning)P(\text{losing}) = 1 - P(\text{winning}) P(losing)=1−37P(\text{losing}) = 1 - \frac{3}{7} P(losing)=77−37P(\text{losing}) = \frac{7}{7} - \frac{3}{7} P(losing)=47P(\text{losing}) = \frac{4}{7}

    The probability of him losing the game is 47\boxed{\frac{4}{7}}.

    : Equilateral Triangle Perimeter

  5. Understand the properties of an equilateral triangle.

    An equilateral triangle has three equal sides. The markings on the diagram confirm this.
    Given that the perimeter is 36 cm and each side is (e+8)(e+8) cm.

  6. Set up an equation for the perimeter.

    Perimeter=3×Side length\text{Perimeter} = 3 \times \text{Side length} 36=3×(e+8)36 = 3 \times (e+8)

  7. Solve the equation for ee.

    Divide both sides by 3:

    363=e+8\frac{36}{3} = e+8 12=e+812 = e+8

    Subtract 8 from both sides:

    e=12−8e = 12 - 8 e=4e = 4

    The value of ee is 4\boxed{4}.

    : Money Calculation

  8. Calculate the number of sh.

    5,000 notes Jamira received.
    The notes are numbered consecutively from BK 1245000 to BK 1245299.
    Number of notes = (Last serial number - First serial number) + 1

    Number of notes=(1245299−1245000)+1\text{Number of notes} = (1245299 - 1245000) + 1 Number of notes=299+1\text{Number of notes} = 299 + 1 Number of notes=300\text{Number of notes} = 300

  9. Calculate the total amount of money.

    Each note is sh. 5,000.

    Total amount=Number of notes×Value per note\text{Total amount} = \text{Number of notes} \times \text{Value per note} Total amount=300×sh. 5,000\text{Total amount} = 300 \times \text{sh. } 5,000 Total amount=sh. 1,500,000\text{Total amount} = \text{sh. } 1,500,000

    The amount of money she was given is sh. 1,500,000\boxed{\text{sh. } 1,500,000}.

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