Question

Sue and barry are trying to find the area of triangle "abc". sue accidentally uses ab and the height from a (instead of the height from c), and barry mistakenly uses bc and the height from c (intead of the height from a). a. sue finds an area of 12 and barry finds an area of 27. what is the true area of triangle "abc"

Answer 1

The true area of triangle ABC is 18 square units.

Step-by-step explanation:

Sue and Barry both attempted to find the area of triangle ABC, but they made errors in their calculations. Sue used the base AB and the height from point A, while Barry used the base BC and the height from point C. To find the correct area of triangle ABC, we need to use the formula for the area of a triangle: (1/2) * base * height. Let's call the height from point C h, and let's assume that Sue's base AB is equal to Barry's base BC.

Using Sue's measurements, we have: (1/2) * AB * h = 12 square units. Rearranging this equation to solve for h, we get: h = (2 * 12) / AB. Substituting this value for h into the formula with Barry's measurements gives us: (1/2) * BC * (2 * 12) / AB = 18 square units. This is our final answer.

So, Sue's calculation was off by a factor of AB / BC, while Barry's calculation was off by a factor of AB / BC as well. If we had known this at the time, we could have corrected their errors and found the correct area more quickly. However, by following the steps carefully and double-checking our calculations, we were able to arrive at the correct answer in the end.

Answer 2

The true area of triangle ABC is 24.

The area of triangle ABC can be determined by using the correct base and height measurements. Sue mistakenly uses AB and the height from A, resulting in an area of 12. Barry, on the other hand, mistakenly uses BC and the height from C, resulting in an area of 27.

To find the true area, we need to find the correct base and height. Let's call the correct base BC and the correct height hC. Since the area is the same, we can set up the equation:

(1/2) * AB * hA = (1/2) * BC * hC

Substituting the given values (12 for Sue's area and 27 for Barry's area) into the equation and solving for BC:

(1/2) * AB * hA = (1/2) * BC * hC

(1/2) * AB * hA = (1/2) * 27 * hC

(1/2) * AB * hA = (1/2) * 12 * hC

Simplifying the equation:

AB * hA = 12 * hC

AB * hA = 6 * (2 * hC)

AB * hA = 6 * BC * hC

AB * hA = BC * hC

Since AB = 2 * BC, we can substitute AB with 2 * BC and simplify the equation:

2 * BC * hA = BC * hC

Cancelling out the BC terms:

2 * hA = hC

So, the true area of triangle ABC can be found by using the correct base BC and height hC. The correct area is twice the area found by Sue and Barry, which means the true area is 2 * 12 = 24.