my last few algebra problems?

Question

2h-6/6 =2/3

write a problem that can be solved by using similar triangles, solve the problem with pictures

Answer 1

(2h-6) /6 = 2/3
multiply all terms by 6 to get rid of denominators
2h - 6 = 4
2h = 10
h = 5

A building 300 ft tall has a 400 ft shadow.
You are 6 ft tall and have a 8 ft shadow.
You measure the distance from the top of your head to the end of your shadow and find that it's 10 ft.
How far is it from the top of the building to the end of its shadow?

Answer 2

Imagine you are making a square shape, say, by nailing studs together to make a wall. Then, before sheathing the wall with plywood, you need to make certain that it is square. The problem then is: How do you ensure that the wall is square?There, are two solutions, that involve the consideration of similar triangles.

solution 1.

Measure the diagonal, left top to bottom right, and compare it to the diagonal, right top to bottom left--they should be equal, if the wall is square. Actually, one first nails the bottom of a wall to a chalk-line that was snapped the width of a 2X4 plus the thickness of the sheathing away from the edge of the floor (for an exterior wall). This ensures that the plates are straight, then, since studs are too short to bend easily, the sides are straight--a prerequisite to squareness.

Solution 2.

On long wall the diagonal method may become impractical, say the diagonal is 27 feet and your tape is only 25 feet long. Then you can use the 3, 4, 5 rule. Simply mark 4 feet away from the corner along the top plate then mark 3 feet down on the stud. Then measure the hypotenuse--the distance between the two marks--and push or pull the top until the distance is 5 feet and the wall is square.

I leave it up to you to see similar triangles are involved. Try drawing a picture first.

Answer 3

1. if 2h - 6/6 = 2/3, then h = 5/6
if (2h - 6) /6 = 2/3, then h = 5

2. Under sunlight, a flag pole casts a shadow 15 feet. At the same time a person 6 feet tall casts a 4 ft shadow. Use similar triangles to find the height of the flag pole.

person
i
i
6ft
i
i
i--shadow- 4ft---

flag pole

i
i
i
i
i
x ft
i
i
i
i
i---shadow--15ft-----------------


6/x = 4/15
90 = 4x
x = 22.5 ft
so, flag pole's height is 22.5 feet

Answer 4

(2h-6) /6 = 2/3
multiply all terms by 6 to get rid of denominators
2h - 6 = 4
2h = 10
h = 5