geometry questions on a practice ACT test

[e^x]

Taher has decided to create a triangular flower bed border. He plans to use 3 pieces of rectangular lumber with lengths 4, 5, and 6 feet, as shown in the figure below. Points A, B, and C are located at the corners of the flower bed.

1. Taher plans to cut the 3 pieces of lumber for the flower bed border from a single piece of lumber. Each cut takes

inch of wood off the length of the piece of lumber. Among the following lengths, in inches, of pieces of lumber, which is the shortest piece that he can use to cut the pieces for the flower bed border?

What's confusing: I don't even know how to start on this one. What do I even do with the info about the 1/8 piece of lumber?

2. After arranging the flower bed, Taher decides that the flower bed would look more attractive if 1 of the angles in the triangle were a right angle. He decides to place the right angle at vertex A and to leave the lengths of AB and AC as 4 and 5 feet, respectively. To the nearest 0.1 foot, how long of a piece of lumber would he need to replace the 6-foot piece represented by BC ?

What's confusing: Isn't A already a right angle?

 

[Dr.Peterson]

1. You didn't list the choices, which may be important. (You may have to choose one that is larger than you really need, but is the best available in the list.)

But the total length of the lumber will be the sum of the lengths of the pieces, plus the amount removed by cutting. How many cuts are needed? What is the total amount removed? What is the total length required?

2. No, A is not a right angle; the picture isn't exact, and you can't judge by that anyway.

If you know enough trigonometry, you can find what angle it is; but for the purposes of the problem, if you use the Pythagorean theorem to find the length of the other side, you'll discover that it is not 6, which proves that A is not currently a right angle!

There is a 3-4-5 right triangle, but not a 4-5-6 right triangle.

 

[Steven G]

When you cut a piece of wood the sum of the length of the two pieces does NOT equal the length of the original piece. Why? Just look on the floor and you will see saw dust. That saw dust is what you lost because of the cut.

Remember that the sum of ALL the parts equals the whole. The total length of the original piece of wood equals the sum of the lengths of the two pieces after you cut it plus the length of piece on the floor (imagine picking up the saw dust and compressing it back together)

Is A a right angle? Maybe. Why guess when Pythagorus can help? Is 6^2 = 5^2 + 4^2? If yes, then A is a right angle and you can keep the 6ft side. If A is not a right angle, make it one. Then y^2= 5^2 + 4^2. Continue from here.