Please do number 1 only

Mathematics

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Answer

13 cm13 \text{ cm}

Step-by-step solution

3 steps

Here's the solution for question 1:

1. In the right-angled triangle ABCABC, AB=12AB = 12 cm and BC=5BC = 5 cm. Find the length of ACAC.

  1. Identify the given sides and the unknown side.

    We are given the lengths of the two legs of the right-angled triangle: AB=12AB = 12 cm and BC=5BC = 5 cm. We need to find the length of the hypotenuse, ACAC.

  2. Apply the Pythagorean theorem.

    For a right-angled triangle, the square of the hypotenuse (AC2AC^2) is equal to the sum of the squares of the other two sides (AB2+BC2AB^2 + BC^2).

    AC2=AB2+BC2AC^2 = AB^2 + BC^2

  3. Substitute the given values and solve for ACAC.

    AC2=122+52AC^2 = 12^2 + 5^2 AC2=144+25AC^2 = 144 + 25 AC2=169AC^2 = 169 AC=169AC = \sqrt{169} AC=13 cmAC = \boxed{13 \text{ cm}}
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