The bottom of a 13-foot straight ladder is set into the ground 5 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach?

the distance of the ladder above the ground is 12 feet.

Step-by-step explanation:

The ladder forms a right angle triangle with the wall and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The distance of the ladder above the ground represents the opposite side of the right angle triangle.

The distance from the bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.

To determine the distance of the ladder above the ground h, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

13² = 5² + h² = 25 + h²

h² = 169 - 25 = 144

h = √144

h = 12 feet

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6