if triangle FGH~ to Triangle PQR, FG = 6, PQ = 10 and the perimeter of trinagle PQR is 35 find the perimeter of triangle FGH
I assume that your wiggle ~ symbol means the triangles are similar. The ratio of the lengths of all corresponding sides is 10/6 = 5/3. PQR therefor has a larger perimeter than FGH by a factor 5/3.
FGH therefore has a perimeter that is 3/5 of 35. That would be 21
yes
Well, since the triangles are similar, we know that the ratios of their corresponding sides are equal. So, we can set up a proportion using the given information.
Let's call the perimeter of triangle FGH "x". That means the perimeter of triangle PQR is 35. Now, since the sides are proportional, we can set up the equation:
FG/PQ = FH/PR = GH/QR
Plugging in the given values, we have:
6/10 = FH/PR = GH/QR
Simplifying this, we get:
3/5 = FH/PR = GH/QR
Now, let's solve for PR.
PR = FH * (5/3)
Since the perimeter is the sum of all the sides, we can express the perimeter of triangle PQR in terms of PR:
35 = PQ + QR + PR
Substituting in the known values, we have:
35 = 10 + QR + FH * (5/3)
Now, we can solve for QR:
QR = 35 - 10 - FH * (5/3)
QR = 25 - FH * (5/3)
Now, let's express the perimeter of triangle FGH in terms of FH:
x = FG + GH + FH
x = 6 + (QR + PR) + FH
x = 6 + (25 - FH * (5/3)) + FH
x = 31 - FH * (5/3) + FH
x = 31 - FH * (2/3)
So, the perimeter of triangle FGH is 31 - FH * (2/3).
To find the perimeter of triangle FGH, we need to know the scale factor between triangle FGH and triangle PQR. Since the triangles are similar, their corresponding sides are proportional.
Let's assume the scale factor between triangle FGH and triangle PQR is 'k'.
Given that FG = 6 and PQ = 10, we can set up a proportion using the corresponding sides:
FG/PQ = FH/PR = GH/QR = k
6/10 = FH/PR
Cross multiplying, we get:
6 * PR = 10 * FH
PR = (10/6) * FH
PR = (5/3) * FH
Now, we can find the lengths of the other sides in terms of FH:
GH = QR = (5/3) * FH
To find the perimeter of triangle PQR, we have:
Perimeter of PQR = PQ + QR + PR
35 = 10 + (5/3) * FH + (5/3) * FH
To find FH, we can rearrange the equation:
35 - 10 = (10/3) * FH + (10/3) * FH
25 = (20/3) * FH
Now, we can solve for FH:
FH = (3/20) * 25
FH = 3.75
Since the perimeter of a triangle is the sum of all its sides, the perimeter of triangle FGH is:
Perimeter of FGH = FG + GH + FH
Perimeter of FGH = 6 + (5/3 * 3.75) + (5/3 * 3.75)
Calculating this, we get:
Perimeter of FGH = 6 + 12.5 + 12.5
Perimeter of FGH = 31
Therefore, the perimeter of triangle FGH is 31 units.