Question

A 26 ft long ramp is used to reach 10 ft up a wall. The ramp covers a horizontal distance of 24 ft. To make the ramp less steep, the horizontal distance is doubled. To reach the same 10 ft height, how long will the ramp need to be? Round your answer to the nearest hundredth.

Answer 1

The length of new ramp is 49.03 ft.

Explanation:

It is given that 26 ft long ramp is used to reach 10 ft up a wall. The ramp covers a horizontal distance of 24 ft.

If the horizontal distance is doubled, then the horizontal distance is 48 ft. The height remains same. Therefore the height of ram is 10 ft.

Use pythagoras in new right angle triangle.

`hypotenuse^2=base^2+perpendicular^2`

`(AE)^2=(AD)^2+(ED)^2`

`(AE)^2=(48)^2+(10)^2`

`(AE)^2=2304+100`

`AE=√(2404)`

`AE=49.0306027\approx 49.03`

Therefore the length of new ramp is 49.03 ft.