The diagram shows a right triangle and three squares. The area of the largest square is 67 units squared.
2 answers:
Answer:
B. 7 and 60
C. 11 and 56
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The area of the three squares must satisfy the Pythagorean Theorem
so
where
c^2 is the area of the largest square
a^2 and b^2 are the areas of the smaller squares
The sum of the areas of the smaller squares must be equal to 67
therefore
7 and 60 ----> could be the areas of the smaller squares (60+7=67)
11 and 56 ----> could be the areas of the smaller squares (11+56=67)
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<h3>Answer: </h3>
The GCF is 4
The polynomial factors to
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Further explanation:
Ignore the x terms
We're looking for the GCF of 12, 4 and 20
Factor each to their prime factorization. It might help to do a factor tree, but this is optional.
- 12 = 2*2*3
- 4 = 2*2
- 20 = 2*2*5
Each factorization involves "2*2", which means 2*2 = 4 is the GCF here.
We can then factor like so
The distributive property pulls out that common 4. We can verify this by distributing the 4 back in, so we get the original expression back again.
The polynomial inside the parenthesis cannot be factored further. Proof of this can be found by looking at the roots and noticing that they aren't rational numbers (use the quadratic formula).