The area of a rhombus is 90 square inches. If the longer diagonal measures 18 inches, what is the length of the shorter diagonal
1 answer:
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Answer:
x = 7
Step-by-step explanation:
The image below shows the relationship between secants chords and tangents.
Imagine that the letters in the image represent the numbers in the actually problem
E would equal 9
C would equal 12
and A would equal x
We would then use the same formula C² = E * ( E + A ) to solve for x , but once again instead of using letters we use the numbers in the problem
We would have 12² = 9( 9 + x )
we now solve for x
Step 1 simplify and distribute
12²=144
9 * 9 = 81
9 * x = 9x
we would then have 144 = 81 + 9x
step 2 subtract 81 from each side
144 - 81 = 63
81 - 81 cancels out
we now have 63 = 9x
step 3 divide each side by 9
63 / 9 = 7
9x / 9 = x
we're left with x = 7
