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A right triangle has sides of 8cm and 15cm. Find the length of the hypotenuse, k.

Using the Pythagorean theorem:

a² + b² = c²

8² + 15² = k²

64 + 225 = k²

289 = k²

k = √289

k = 17cm

Answer :

To find the length of the hypotenuse in a right triangle where the other two sides are known, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The formula is given by:
[tex]a^2 + b^2 = c^2[/tex]

In this problem, the lengths of the two known sides are 8 cm and 15 cm. Let's denote the side lengths as [tex]a = 8 \text{ cm}[/tex] and [tex]b = 15 \text{ cm}[/tex]. The length of the hypotenuse, which we need to find, is [tex]k[/tex] (equivalent to [tex]c[/tex] in the theorem).

  1. Substitute the known values into the Pythagorean theorem:
    [tex]8^2 + 15^2 = k^2[/tex]

  2. Calculate the squares of the two known sides:
    [tex]8^2 = 64[/tex]
    [tex]15^2 = 225[/tex]

  3. Add these squares together:
    [tex]64 + 225 = 289[/tex]

  4. Thus, the equation for [tex]k^2[/tex] is:
    [tex]k^2 = 289[/tex]

  5. To find [tex]k[/tex] (the length of the hypotenuse), take the square root of both sides:
    [tex]k = \sqrt{289}[/tex]

  6. Calculate the square root:
    [tex]k = 17 \text{ cm}[/tex]

Thus, the length of the hypotenuse is 17 cm.

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