Question

Troy is building a ramp for his toy cars. the plank he is using for the ramp is 5 feet long and is placed on a 3-foot-high box. a diagram shows troy’s box and ramp make a polygon made up of a square and right triangle. the square is 3 feet on each side. the right triangle joins the square so 3 feet is the height of the triangle. the hypotenuse is 5 feet. the last side, labeled b, is unknown. how far from the box is the bottom edge of troy's ramp, in feet?

Answer 1

The distance between the box and the bottom edge of Troy's ramp is 4 feet.

Step-by-step explanation:

Troy's ramp consists of a square and a right triangle. The square has sides of 3 feet, and the triangle has a height of 3 feet and a hypotenuse of 5 feet. We need to find the distance between the box and the bottom edge of the ramp, which is the unknown side labeled 'b'.

Using the Pythagorean theorem, we can solve for 'b'. The theorem states that in a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse. So, b² + 3² = 5². Simplifying this equation gives us b² + 9 = 25. Subtracting 9 from both sides, we get b² = 16. Taking the square root of both sides, we find that b = ±4. Since 'b' represents a length, we take the positive value, so b = 4 feet.

Therefore, the bottom edge of Troy's ramp is located 4 feet away from the box.