A 10-foot straight ladder leans against a vertical wall on flat horizontal ground. If the … — GRE General Test

A $10$ -foot straight ladder leans against a vertical wall on flat horizontal ground. If the bottom of the ladder is $6$ feet away from the base of the wall, how high up the wall, in feet, does the top of the ladder reach?

Answer: 8 feet

Answer

The top of the ladder reaches

8

feet up the wall.

Applying the Pythagorean theorem

a^2 + b^2 = c^2

with hypotenuse

c = 10

and ground leg

a = 6

gives

6^2 + b^2 = 10^2

, which simplifies to

36 + b^2 = 100

, so

b^2 = 64

and

b = 8

feet.

Step-by-Step Solution

Set up the right triangle relationship using the Pythagorean theorem.

a^2 + b^2 = c^2

, where

a = 6

and

c = 10

The ladder forms the hypotenuse of a right triangle with the vertical wall and horizontal ground.

Substitute the known values into the formula and solve for

b

6^2 + b^2 = 10^2 \implies 36 + b^2 = 100 \implies b^2 = 64 \implies b = 8

Subtracting

36

from

100

gives

64

, and taking the positive square root yields the vertical height.

Key Concept

Applying the Pythagorean Theorem (

a^2 + b^2 = c^2

) to find an unknown leg length in a right triangle context.

Question

Answer

Step-by-Step Solution

Key Concept

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