Answer:
13.9 ft
Step-by-step explanation:
Please find the attachment.
Let x be the length of the ramp.
We have been given that a building has a ramp to its front doors to accommodate the handicapped. The distance from the building to the end of the ramp is 13 feet and the height from the ground to the front doors is 5 feet.
We can see from our diagram that the ramp makes a right triangle with the height of the door and ground. We can also see that length of the ramp will be the hypotenuse of our right triangle.
So we will use Pythagoras theorem to find the length of the ramp.
[tex]\text{Hypotenuse}^2=\text{(Leg 1)}^2+\text{(Leg 2)}^2[/tex]
Upon substituting our given values we will get,
[tex]x^2=\text{(13 ft)}^2+\text{(5 ft)}^2[/tex]
[tex]x^2=169\text{ ft}^2+25\text{ ft}^2[/tex]
[tex]x^2=194\text{ ft}^2[/tex]
Let us take square root of both sides of our equation.
[tex]x=\sqrt{194\text{ ft}^2}[/tex]
[tex]x=13.928\text{ ft}\approx 13.9\text{ ft}[/tex]
Therefore, the ramp is 13.9 feet long.
