Q:

triangles IJK and TUV are similar.The length of the sides of IJK are 40, 50, and 24. The length of the longest side of TUV is 275 what is the perimeter of TUV?

Accepted Solution

A:
The perimeter of triangle TUV which is similar to the triangle IJK is 627 units.What is perimeter of plane?The measure of the boundary of a plane or shape is called its perimeter. The perimeter of a plane or shape is the sum of all the sides.Triangles IJK and TUV are similar. The length of the sides of IJK are 40, 50, and 24. Let the corresponding side whose length is 40 is x. The longest side of the triangle IJK is 50 and the longest side of the triangle TUV is 275. Thus, the ratio of these side should be equal for the similar triangle,[tex]\dfrac{x}{40}=\dfrac{275}{50}\\x=220[/tex]Let the corresponding side whose length is 24 is y in the similar triangle. Again the ratio,[tex]\dfrac{y}{24}=\dfrac{275}{50}\\y=132[/tex]Hence, the length of the triangle TUV are 220, 132 and 275 units. The perimeter of it is,[tex]P=220+ 132 +275 \\P=627\rm\; units[/tex]Hence, the perimeter of triangle TUV which is similar to the triangle IJK is 627 units.Learn more about the perimeter of plane here;