9514 1404 393
Answer:
a) yes; 12/15/17 ~ 20/25/x; SAS
b) x = 28 1/3
Step-by-step explanation:
The left-side segments are in the ratio ...
top : bottom = 12 : 8 = 3 : 2
The right side segments are in the ratio ...
top : bottom = 15 : 10 = 3 : 2
These are the same ratio, and the angle at the peak is the same in both triangles, so the triangles are similar by the SAS postulate.
Normally, a similarity statement would identify the triangles by the labels on their vertices. Here, there are no such labels, so we choose to write the statement in terms of the side lengths, shortest to longest:
12/15/17 ~ 20/25/x
__
The sides of similar triangles are proportional, so the ratio of longest to shortest sides will be the same in the two triangles. In the smaller triangle, the longest side is 17/12 times the length of the shortest side. The value of x will be 17/12 times the length of the shortest side in the larger triangle:
x = 17/12 · 20 = 340/12
x = 28 1/3
Answer:
Step-by-step explanation:
You need to specify what the goal of the problem is.
If Kai picked 7 times as many blueberries as Nico, then:
n + 7n + 297, or
8n = 297. Unfortunately, 8 does not divide evenly into 297, and we certainly are not interested in picking fractional blueberries.
If the problem mentioned 296 instead of 297 total blueberries, then
Nico (n) picked 47 blueberries and Kai picked 7 times that many, or 329.
