6.
B
C
Given: rhombus ABCD with diagonals drawn.
E
AE = 2/3 * x and EC = x - 10
Find the value of x.
Remember:
• Don't let fractions throw you. Use your algebra skills! If you don't like working with the fraction, multiply each term of the equation by the denominator value to eliminate the fraction from the problem.
• While this problem gave you a rhombus, it was not expecting the use of a property specific to a rhombus. The needed property is that the diagonals bisect each other - a property held by both parallelograms and rhombuses.
B
C
Given: rhombus ABCD with diagonals drawn.
E
AE = 2/3 * x and EC = x - 10
Find the value of x.
Remember:
• Don't let fractions throw you. Use your algebra skills! If you don't like working with the fraction, multiply each term of the equation by the denominator value to eliminate the fraction from the problem.
• While this problem gave you a rhombus, it was not expecting the use of a property specific to a rhombus. The needed property is that the diagonals bisect each other - a property held by both parallelograms and rhombuses.
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Answer:
Since AE and EC are diagonals of the rhombus, they bisect each other. Therefore, we can set AE equal to EC and solve for x:
AE = EC
2/3 * x = x - 10
Multiplying both sides by 3, we get:
2x = 3(x - 10)
Expanding the right side, we get:
2x = 3x - 30
Subtracting 2x from both sides, we get:
x = 30
Therefore, the value of x is 30.