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A wire fence is to be strung from the top of one wall to the top of another wall. The walls are perpendicular to each other and are 18 m and 24 m high. How long must the wire be?

Mathematics

ScanSolve AI Answer

Answer

30 m\text{30 m}

Step-by-step solution

6 steps

  1. Identify the given values from the problem.

    The lengths of the two walls (legs of the right-angled triangle) are given as b=18b = 18 m and c=24c = 24 m. The length of the wire fence (hypotenuse) is aa.

  2. Apply the Pythagorean theorem.

    The formula for the Pythagorean theorem is given as a2=b2+c2a^2 = b^2 + c^2.

  3. Substitute the given values into the formula.

    a2=(18 m)2+(24 m)2a^2 = (18\, \text{m})^2 + (24\, \text{m})^2

  4. Calculate the squares of the given lengths.

    a2=324 m2+576 m2a^2 = 324\, \text{m}^2 + 576\, \text{m}^2

  5. Add the squared values.

    a2=900 m2a^2 = 900\, \text{m}^2

  6. Solve for aa by taking the square root of both sides.

    a=900 m2a = \sqrt{900\, \text{m}^2} a=30 ma = 30\, \text{m}

    The length of the wire fence (a) is 30 m.

    30 m\text{30 m}
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