Question

In rhombus ABCD, diagonals AC and BD intersect at M. If AM=x+ 3y, BM=x+ 6, Mc= 3x- 9, and DM =2y +8, how do you find the values of x and y?

Answer 1

Values of `x=12 and y=5`

Explanation:

The diagonals of a rhombus bisect each other. This means that they cut each other in half.

So `AM=CM and BM=DM :. AM=CM or x+3y=3x-9 or 2x-3y =9 (1)`
`BM=DM or x+6=2y+8 or x-2y =2 (2)`

Multiplying equation(2) by 2 and then subtrating from equation (1) we get , `2x-3y =9 (1)`
`2x-4y =4 (2)`
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`y=5 :. x=2y+2=10+2=12`

Values of `x=12 and y=5` [Ans]