A 9 foot ladder leans against a building at a point 7 feet above the ground. At what height would a 15 foot ladder touch the building if both ladders for the same angle with the ground?

Propotion? But I just get a decimal...

I got 11 and 2/3rds, correct?

x/7 = 15/9

x = 105/9 = 11 2/3

you are correct

Thanks Reiny.

To solve this problem using proportions, we can set up a ratio between the lengths of the ladders and the heights they touch on the building.

Let's define:
- x as the height on the building where the 15-foot ladder touches.

We have the following proportional relationship:
9 feet (length of the 9-foot ladder) : 7 feet (height on the building) = 15 feet (length of the 15-foot ladder) : x (height on the building)

Writing this as a proportion, we get:
9/7 = 15/x

To solve for x, we can cross-multiply and then divide:
9x = 7 * 15
9x = 105
x = 105/9
x = 11.67 feet

Therefore, if both ladders are at the same angle with the ground, a 15-foot ladder would touch the building at a height of approximately 11.67 feet.