A perfect square must be hidden within all of those radicands in order to simplify them down to what the answer is.
.
.
. The rules for adding radicals is that the index has to be the same (all of our indexes are 2 since we have square roots), and the radicands have to be the same. In other words, we cannot add the square root of 4 to the square root of 5. They either both have to be 4 or they both have to be 5. So here's what we have thus far:
. We can add
and
to get
. That means as far as our answer goes, A = 72 and B = 4, or (72, 4), choice a.
The triangles given below in the diagram are similar by; D: The SSS Similarity theorem.
<h3>How to interpret similar triangles?</h3>
From triangle similarity theorems, we know that;
If a segment is parallel to one side of a triangle and intersects the other two sides, then the triangle formed is similar to the original and the segment that divides the two sides it intersects is proportional.
Now, from the given diagram, we see the ratio of corresponding sides are congruent as;
45/30 = 54/36 = 36/24 = 1.5
Thus, the triangles are similar by SSS similarity theorem
Read more about Similar Triangles at; brainly.com/question/14285697
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Answer:
45 and 135
Step-by-step explanation:
If angles, with measurements a and b, are supplementary, then a and b have sum 180 degrees.
So we have the following equation so far:
a+b=180
Now we also have that one angle has a measurement that is 1/3 the value of the one.
So we also have 3a=b which means we are letting the angle whose measurement be a have 1/3 the value of b.
So lets plug the second equation into first giving us:
a+3a=180
Add like terms:
4a=180
Divide both sides by 4:
a=180/4
a=45
So b=3a=3(45)=135.
So the angles in question have measurement s 45 and 135.
