Liev is assembling a coffee table. The diagram below is from the instruction manual and shows the table after the first two legs have been attached.
The next step in assembling the coffee table is to attach a support from point D to point C, which is halfway down leg A.
The table legs are each 18 inches tall. What is the length of the support?
A. 41 inches
B. 44 inches
C. 49 inches
D. 40 inches
To find the length of the support, we first need to find the distance from point D to the midpoint between points A and B. Since each leg is 18 inches tall, the distance from D to the midpoint is 18 inches.
Next, we can use the Pythagorean theorem to find the length of the support. We can treat the support as the hypotenuse of a right triangle with legs of 18 inches and half of the distance between legs A and B.
Using the Pythagorean theorem:
a^2 + b^2 = c^2
18^2 + (18/2)^2 = c^2
324 + 81 = c^2
405 = c^2
c = √405
c ≈ 20.1 inches
Since the support goes from point D to halfway between points A and B:
Support length = 18 inches (distance from D to mid-point of A and B) + 20.1 inches (length of the hypotenuse)
Support length = 38.1 inches
Therefore, the nearest option is:
D. 40 inches