Rhombus ABCD has an area of 264 square units. If DB=12 units find AC.

So far this is what I have-
1/2(264)=132 132/2=66
66-12=44units
Is this the correct process?

I don't follow your work.

Sketch the rhombas. One diagonal is 12, so half that diagonal is 6.

call that half b, so 2b=12
now call half the other diagonal a
so the length of that diagonal is 2a, and that is what you are looking for.

Now, the diagonals of a rhombus are perpendicular bisectors, so you have four right triangles, the area of which is
1/2 a b=264/4
or ab=132, but a=6, so a=22
which means 2a=44, so your answer is correct.

Well, you're on the right track, but let me put it in a way that's a bit more fun!

So, we know that the area of the rhombus is 264 square units. That's like saying it's baked to perfection with 264 units of deliciousness! Now, let's find the length of AC, or "Awesomeness Central"!

Since a rhombus has equal diagonals, we can split it into four congruent triangles. And the area of each triangle will be half of the area of the rhombus. So, each triangle will have an area of 132 square units, which is like having 132 units of triangle-tastic goodness!

Now, we know that DB, or "Diagonal Buddy," is 12 units. So, we need to find AC, or "Awesome Connection." But don't worry, we won't leave DB feeling lonely!

By splitting the rhombus into two congruent triangles, we have DB as the base, and AC as the height of each triangle. Since the area of each triangle is 132 square units, we can use the formula for the area of a triangle:

Area = (base * height) / 2

Plugging in the values, we have:

132 = (12 * AC) / 2

Now, let's work some magic and solve this equation:

132 = 6AC

Divide both sides by 6:

AC = 22 units

So, the length of AC, or "Awesome Connection," is 22 units. Now, our rhombus is all set to spread its awesomeness everywhere!

The process you have followed is not correct. Allow me to guide you step-by-step.

1. Recall that the area of a rhombus is given by the formula: Area = 1/2 * d1 * d2, where d1 and d2 are the diagonals of the rhombus.

2. In this case, you have the area of the rhombus as 264 square units and one diagonal DB as 12 units.

3. Let's denote the other diagonal as DA.

4. Using the formula for the area of a rhombus, we can write the equation: 264 = 1/2 * DB * DA.

5. Substituting the value of DB as 12 units, we get: 264 = 1/2 * 12 * DA.

6. Simplifying the equation, we have: 264 = 6 * DA.

7. Divide both sides by 6 to isolate DA: DA = 264/6 = 44 units.

Therefore, the length of the other diagonal, AC, is equal to 44 units.

The process you followed is not correct. Let me explain how to find the length of AC in a rhombus.

In a rhombus, the diagonals are perpendicular bisectors of each other. This means that DB is not just any side of the rhombus, but it is actually a diagonal. Let's call the point of intersection of the diagonals as point O.

Since the diagonals of a rhombus bisect each other and are perpendicular, we can divide the rhombus into four congruent right triangles. In this case, triangle AOD is one of those triangles.

Now, we can find the area of triangle AOD by using the formula for the area of a triangle, which is 1/2 * base * height.

The base of triangle AOD is DB, which has a length of 12 units. The height of triangle AOD is half of AC, let's call it h.

Now, we can rewrite the formula for the area of triangle AOD: 1/2 * 12 * h = 264.

Simplifying the equation: 6h = 264.

Dividing both sides by 6: h = 44.

Since h is half of AC, we can find AC by multiplying h by 2: AC = 2 * 44 = 88.

So, the length of AC in rhombus ABCD is 88 units.