Question

You have a steel wire that is 104 inches long. To make a sign holder, you bend the wire x inches from each end to form two right angles. To use the sign holder, you insert each end 6 inches into the ground.

Answer 1

Length of the sign holder, including the two right angles and the 6 inches inserted into the ground, is 71 inches.

Step-by-step explanation:

To determine how far to bend the wire from each end, we need to first calculate the length of the two right angles. Since a right angle is 90 degrees, we can use the trigonometric formula for a right triangle to find the length of each side.

Let's call the length of the wire between the two right angles "x". We know that the sum of the lengths of the sides of a triangle must equal the length of the wire, so we can set up the equation:

x + x + 6 = 104

Simplifying this equation, we get:

2x + 6 = 104

Subtracting 6 from both sides, we get:

2x = 98

Dividing both sides by 2, we get:

x = 49

So, we need to bend the wire 49 inches from each end to form two right angles. This will result in a sign holder with a total length of 83 inches.

To insert each end 6 inches into the ground, we can simply subtract 6 inches from the total length of the sign holder, which gives us:

83 - 6 - 6 = 71

Therefore, the final length of the sign holder, including the two right angles and the 6 inches inserted into the ground, is 71 inches.