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Korir constructed a ramp leading to his granary store to make it easier to transport bags of grain into storage after harvest. The ramp reaches a height of 4 m above ground and has a length of 10 m, as shown in the diagram below. Calculate the value of x

Mathematics

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Answers

2 parts
9

x≥20 and x≤45x \ge 20 \text{ and } x \le 45

10

221 m2\sqrt{21} \text{ m}

Step-by-step solution

8 steps

Part 9· 2 steps

  1. Interpret "at least 20".

    This means the number of learners, xx, must be greater than or equal to 20.

    x≥20x \ge 20

  2. Interpret "not more than 45".

    This means the number of learners, xx, must be less than or equal to 45.

    x≤45x \le 45

    The two simple inequality statements are:

    x≥20 and x≤45\boxed{x \ge 20 \text{ and } x \le 45}

Part 10

221 m2\sqrt{21} \text{ m}

  1. Identify the type of triangle and the relevant theorem.

    The diagram shows a right-angled triangle. We can use the Pythagorean theorem, which states a2+b2=c2a^2 + b^2 = c^2, where aa and bb are the lengths of the legs and cc is the length of the hypotenuse.

  2. Substitute the given values into the Pythagorean theorem.

    Here, the height is 4 m4 \text{ m} (one leg), the base is xx (the other leg), and the ramp length is 10 m10 \text{ m} (the hypotenuse).

    42+x2=1024^2 + x^2 = 10^2

  3. Calculate the squares.

    16+x2=10016 + x^2 = 100

  4. Isolate x2x^2.

    x2=100−16x^2 = 100 - 16 x2=84x^2 = 84

  5. Solve for xx by taking the square root.

    x=84x = \sqrt{84}

  6. Simplify the square root.

    x=4×21x = \sqrt{4 \times 21} x=221x = 2\sqrt{21}

    The value of xx is 221 m2\sqrt{21} \text{ m}.

    221 m\boxed{2\sqrt{21} \text{ m}}
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