Andy has two rectangular gardens. His smaller garden is 8 feet long and 4 feet wide. The larger garden is 12 feet long and six feet wide. Which statement correctly describes Andy gardens?

Question

anonymous · Answer

A)
The gardens are only congruent.	
B)
The gardens are similar and congruent.	
Eliminate
C)
The gardens are congruent, but not similar.	
D)
The gardens are similar, but not congruent.

anonymous · Answer

Well, if we write a proportion for each of the gardens:$$\frac{ 4 }{ 8 }$$ and $$\frac{ 6 }{ 12 }$$ They can both be simplified down to 1/2. They are clearly not congruent since they are different lengths.

anonymous · Answer

Does that mean the answers D?

anonymous · Answer

Correct.

anonymous · Answer

Thank You! :)

anonymous · Answer

No problem :)

anonymous · Answer

@AnonymousBeast is correct that they certainly are not congruent. If the two garden were congruent, the individual measurements for length and width would be exactly the same. However, I propose setting up proportions of the length of Garden A to length of Garden B and the same for the width...
ie.  $$\frac{ 8 }{ 12 } = $$
and $$\frac{ 4 }{ 6 }=$$

If you reduce them both, you get $$\frac{ 2 }{ 3 } and \frac{ 2 }{ 3 }$$.
These are EQUAL PROPORTIONS. Therefore, because they are proportionate to one another, the two gardens are SIMILAR.

anonymous · Answer

If there were an additional answer choice of Neither congruent, nor similar, you would have to do this step in order to determine whether or not they are actually similar.

anonymous · Answer

Oh ok thanks for the response :)

anonymous · Answer

@bcgfghg  You're welcome.

anonymous · Answer

Wanna answer this one too i think its right.
	
Which type of triangle has side lengths of 2 in, 5 in, and 6 in?
A)
acute	
Eliminate
B)
equilateral	
C)
obtuse	
D)
right

@TOMWALK @AnonymousBeast

anonymous · Answer

Well, it cannot be equilateral because the sides are not the same length. Nor can it be a right triangle because: According to the Pythagorean Theorem $$2^2+5^2=6^2$$But, it does not because $$29\neq36$$ So B and D are eliminated.

anonymous · Answer

In order for a triangle to be a right triangle, the Pythagorean theorem needs to apply. In other words: The sum of the squares of the two shorter sides must equal the square of the longest side, which is the hypotenuse.

anonymous · Answer

@AnonymousBeast is correct.

anonymous · Answer

The answer was obtuse which is what I picked based on your guys help. Thanks

anonymous · Answer

Yes it was, my apologies, it was taking me a bit of time to type.