51:30
1 answer:
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Similar triangles are triangles that have the same interior angles and the corresponding sides are proportional, that is, for triangles STU and XYZ we have the proportion:
The corresponding sides are congruent only if the proportion rate is 1, but that is not always true and it's not necessary.
Therefore the correct option is B: False
If the corresponding sides are congruent, the triangles are congruent.
Answer:
Step-by-step explanation:
Convert the above mixed numbers to improper fractions through this simple approach: 3 × 10 + 1 /10 = 31/10. Similarly, 2 × 6 + 5 /6 = 17/6
Take the LCM of the denominators and simplify. LCM = 60. Thus, 60/10 = 6; 6 × 31 = 186. Also, 60/6 =10; 10×17 =170 all divide by 60:
Common factors between the numerator and denominator is 4, therefore 16/4 = 4 and 60/4 = 15.
Therefore the answer is 4/15 in simplest form.
Each petal of the region 
is the intersection of two circles, both of diameter 10. Each petal in turn is twice the area of a circular segment bounded by a chord of length 
, which implies the segment is subtended by an angle of 
. This means the area of the segment is
This means the area of one petal is
, and the area of is four times this, or 
.
Meanwhile, the area of
is simply the area of the square minus the area of , or 
.
So
(provided these regions are indeed disjoint; it's hard to tell from the picture)
This means the area of one petal is
Meanwhile, the area of
So