Question

An 8.5-meter ladder is leaning against a vertical wall. How many meters is its base from the wall if the ladder reaches 7.5 meters up the wall?

Answer 1

4

Explanation:

We have a right triangle where the ratio of one leg to the hypotenuse is $15:17$. Since 8, 15, 17 is a Pythagorean triple, the ratio of the other leg to the hypotenuse must be $8:17$. If the length of this leg is $x$, this means that $x/8.5 = 8/17$. It follows that $x = \boxed4$ meters.

Answer 2

4 m

Explanation:

The geometry is that of a right triangle with hypotenuse 8.5 m and one side of length 7.5 m. If "b" represents the distance from the base of the ladder to the wall, the Pythagorean theorem tells us ...

b² + 7.5² = 8.5²

b² + 56.25 = 72.25

b² = 16 . . . . . . . . . . . . . subtract 56.25

b = 4 . . . . meters . . . (take the square root)

The base of the ladder is 4 m from the wall.

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You may recognize this as the 8-15-17 Pythagorean triple, scaled by 1/2.