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Problem 1149

# The area of a rhombus is equal to the area of a square whose side is $$6 .$$ If the length of one diagonal of the rhombus is 8 , how long is the other diagonal?

Expert verified
The length of the other diagonal of the rhombus is $$9$$.
See the step by step solution

## Step 1: Find the area of the square

The area of a square is calculated as side^2. We are given the side of the square to be 6, so we can find its area: $$A = 6^2 = 36$$.

## Step 2: Find the area of the rhombus

We are given that the area of the rhombus is equal to the area of the square. So, the area of the rhombus is also 36.

## Step 3: Use the area formula for rhombus

The area of a rhombus can be calculated as: $$A = (d1 * d2) / 2$$, where d1 and d2 are the lengths of the diagonals. We know one diagonal length (8) and the area (36). Now we need to find the length of the other diagonal (d2). Set up the equation: $$36 = (8 * d2) / 2$$

## Step 4: Solve for the length of the other diagonal

We have the formula for the area of the rhombus with the values: $$36 = (8 * d2) / 2$$. Now, we need to solve for d2. First, multiply both sides of the equation by 2 to get rid of the fraction: $$72 = 8 * d2$$ Now, divide both sides by 8 to find d2: $$d2 = 72 / 8$$ $$d2 = 9$$ The length of the other diagonal is 9.

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