a The order of the wording is important here. Which side length should be in the denominator and the numerator of your fraction?
B
b Calculate the ratio of the two triangles perimeters.
C
c Use the similarity between the triangles to calculate EC.
A
a 4
B
b It is the same.
C
c 28 feet
Practice makes perfect
a We are asked to calculate the ratio of side length NE to side length AK. This means that we should divide NE by AK and not the other way around.
NE/AK=96/24=4
With this, we know that NE is four times the length of AK.
b To calculate the perimeter, we need to know all three sides of our triangles. Note that both of them are isosceles triangles. With this, we can find the length of the third side which has been marked as congruent with another side in each triangle.
To determine the last unknown side, EC, we can use the similarity between the two triangles to write an equation.
EC/7=96/24
Let's solve this equation.
When we know all of the sides in both triangles, we can calculate their perimeters.
Perimeter â–³ KRA:& 24+24+7=55 feet
Perimeter â–³ ENC:& 28+96+96=220 feet
Now we can compare the perimeters of â–³ ENC and â–³ KRA.
Perimeterâ–³ ENC/Perimeter â–³ KRA=220/55=4
As we can see, the ratio of the perimeter of â–³ ENC to â–³ KRA is equal to the ratio of the side lengths.
c In Part B, we had to find the length of EC to determine the perimeter of â–³ ENC. To do that, we set up an equation using the fact that the triangles are similar. Let's redo this calculation.
