SOLUTION: One diagonal of a rhombus is increased by 24%. By what percent should the other diagonal be decreased so that the area of the rhombus is unchanged?

Question 1093104: One diagonal of a rhombus is increased by 24%. By what percent should the other diagonal be decreased so that the area of the rhombus is unchanged?
Answer by greenestamps(13209) (Show Source): You can put this solution on YOUR website!

The area of a rhombus is half the product of the diagonals. If the area is to remain unchanged when the length of one diagonal increases, the length of the other diagonal need to decrease proportionally.

When we talk about proportions, the operation we are using is multiplication, not addition. So when the problem says the length of one diagonal is increased by 24%, then instead of thinking of adding 24%, think of multiplying by 124%, or 1.24.

Now, if the length of one diagonal is multiplied by 1.24, and the area of the rhombus is to remain unchanged, the length of the other diagonal needs to be divided by 1.24, which means muliplied by 1/1.24.

1 divided by 1.24 is approximately 0.80645...,or about 80.645%.

The problem asks for an answer in terms of the percentage by which the length of the second diagonal needs to be decreased. But multiplying the length by 80.645% means decreasing its length by (100-80.645)%, or 19.355%.
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