SOLUTION: A designer of decorative tiles wants to have some custom tiles made in the shape of a rhombus, with one diagonal twice the length of the other. If each side of a tile is to be 12 i

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Question 1083257: A designer of decorative tiles wants to have some custom tiles made in the shape of a rhombus, with one diagonal twice the length of the other. If each side of a tile is to be 12 inches long, what will be the length of its shorter diagonal, to the nearest hundredth of an inch?
Select one:
a. 8.00 in
b. 10.73 in
c. 5.37 in
d. 21.47 in

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

given:
d%5B1%5D=2d%5B2%5D where d%5B2%5D is shorter diagonal
a=12in
side, and half of each diagonal form right triangle, so use Pythagorean theorem
12%5E2=%28d%5B1%5D%2F2%29%5E2%2B%28d%5B2%5D%2F2%29%5E2
144=%282d%5B2%5D%2F2%29%5E2%2B%28d%5B2%5D%2F2%29%5E2
144=%28d%5B2%5D%29%5E2%2B%28d%5B2%5D%29%5E2%2F4
144=%285%2F4%29%28d%5B2%5D%29%5E2
144%2F%285%2F4%29=%28d%5B2%5D%29%5E2
115.2=%28d%5B2%5D%29%5E2
d%5B2%5D=sqrt%28115.2%29
d%5B2%5D=10.73
answer is: b. 10.73in