Strange problem ive encountered!!

[gusrohar]

Hi, I am currently studying for Högskoleprovet, the swedish equivalent of the SATS.

There is an assignment where I have to figure out the are of a triangle that is uniform with another.

Triangle T1 has a side 12cm adjacent to an angle theta. T1 has an area of 72cm.
Triangle T2 has a sideof 8 cm adjacent to an angle theta. T2 has an unknown area.

My answer is that the area is 48 cm while the answer on the graded tests are 32. What am i missing?

 

[stapel]

I have to figure out the are of a triangle that is uniform with another.

I'm going to assume that "uniform" means "similar".

Triangle T1 has a side 12cm adjacent to an angle theta. T1 has an area of 72cm.
Triangle T2 has a sideof 8 cm adjacent to an angle theta. T2 has an unknown area.

My answer is that the area is 48 cm while the answer on the graded tests are 32. What am i missing?

What were your steps in arriving at your answer? How did you take into account the fact that linear measures (of lengths of sides, for instance) are not quite the same as square measures (such as areas of triangles)?

Please be complete. Thank you!

 

[wjm11]

Hi, I am currently studying for Högskoleprovet, the swedish equivalent of the SATS.

There is an assignment where I have to figure out the are of a triangle that is uniform with another.

Triangle T1 has a side 12cm adjacent to an angle theta. T1 has an area of 72cm.
Triangle T2 has a sideof 8 cm adjacent to an angle theta. T2 has an unknown area.

My answer is that the area is 48 cm while the answer on the graded tests are 32. What am i missing?

Consider a rectangle that is 3x5; its area is 15.
Consider a rectangle that is 6x10; its area is 60.
We can see that the first rectangle's side lengths were doubled to create the second rectangle. What was the effect on area?

 

[gusrohar]

Alright these are my calculations. Since the test is taken without calculator I will not be using a calculator to solve any problem.

t1 uniform with t2 <=> 12/72 = 8/x where x is the area of t2. I evaluate x to 48 cm. But since im very very dumb sometimes and miss the simplest things ive probably made a mistake here aswell!

 

[gusrohar]

Consider a rectangle that is 3x5; its area is 15.
Consider a rectangle that is 6x10; its area is 60.
We can see that the first rectangle's side lengths were doubled to create the second rectangle. What was the effect on area?

After reading this and the other replies I am hinting towards my mistake being that altough sides may be uniform, the areas may not!

Since: 3/15 =//= 6/60 which was the method i calculated my answer.

Edit: The areas may be similar or uniform (whichever word is correct) but they may have a different ratio than the ratio of the sides?

 

[gusrohar]

I found an equation with a quick google search which said that the ratio between the sides squared equals the ratio between the areas. However no explanation of why this is.

 

[wjm11]

Hi, I am currently studying for Högskoleprovet, the swedish equivalent of the SATS.

There is an assignment where I have to figure out the are of a triangle that is uniform with another.

Triangle T1 has a side 12cm adjacent to an angle theta. T1 has an area of 72cm.
Triangle T2 has a sideof 8 cm adjacent to an angle theta. T2 has an unknown area.

My answer is that the area is 48 cm while the answer on the graded tests are 32. What am i missing?

Let me expand on my previous hint/example:

Consider a rectangle that is 3x5; its area is 15.
Consider a rectangle that is 6x10; its area is 60.
We can see that the first rectangle's side lengths were doubled to create the second rectangle. What was the effect on area?
Answer: When the sides were 2 times bigger, the area was 4 times bigger.

Continuing along this train of thought, consider a 9x15 triangle. Its area is 135.
When the sides of the triangle are 3 times bigger, the area is 9 times bigger.

What these examples demonstrate is that when the sides are increased or decreased by some factor, the area will be changed by the square of that factor.

In you case, the factor is (8/12) = (2/3). Therefore the area of the smaller triangle will be ((2/3)^2)(72) = (4/9)(72) = 32

 

[stapel]

After reading this and the other replies I am hinting towards my mistake being that altough sides may be uniform, the areas may not!

Given that figures m and M are similar, with heights h and H and areas a and A, respectively, what proportions can you create? In particular, how does the ratio of heights relate to the ratio of areas? (Check here for specifics.)

 

[gusrohar]

Let me expand on my previous hint/example:

Consider a rectangle that is 3x5; its area is 15.
Consider a rectangle that is 6x10; its area is 60.
We can see that the first rectangle's side lengths were doubled to create the second rectangle. What was the effect on area?
Answer: When the sides were 2 times bigger, the area was 4 times bigger.

Continuing along this train of thought, consider a 9x15 triangle. Its area is 135.
When the sides of the triangle are 3 times bigger, the area is 9 times bigger.

What these examples demonstrate is that when the sides are increased or decreased by some factor, the area will be changed by the square of that factor.

In you case, the factor is (8/12) = (2/3). Therefore the area of the smaller triangle will be ((2/3)^2)(72) = (4/9)(72) = 32

See I understand what your saying. But I don't understand why it is that way. The reason I'm asking is this question is supposed to be answered within a minute. Imagine calculating the ratio of 12/8, squaring it and then dividing 72 by it. I was hoping there would be a simpler way to see it.