Triangle DEF ~ Triangle HJK, and the scale factor of Triangle DEF to Triangle HJK is 5/2. If EF=15, find JK
solve
15/JK = 5/2
To find JK, we can use the scale factor to set up the ratio of corresponding sides between the two triangles.
The scale factor of Triangle DEF to Triangle HJK is 5/2. This means that each side of TriangleDEF is 5/2 times the length of the corresponding side in Triangle HJK.
EF corresponds to JK, so we can set up the ratio:
EF/JK = 5/2
Substituting EF = 15:
15/JK = 5/2
To solve for JK, we can cross-multiply and solve for JK:
2 * 15 = JK * 5
30 = JK * 5
Now we can isolate JK by dividing both sides of the equation by 5:
30/5 = JK
JK = 6
Therefore, JK is equal to 6.
To find the length of JK, we need to set up a proportion using the scale factor.
The scale factor is defined as the ratio of corresponding side lengths of the two similar triangles.
In this case, the scale factor of Triangle DEF to Triangle HJK is given as 5/2. This means that each side length of Triangle HJK is 5/2 times the corresponding side length of Triangle DEF.
Therefore, we can set up the proportion:
EF / JK = 5/2
Plugging in the given values, we have:
15 / JK = 5/2
To solve for JK, we can cross multiply:
2 * 15 = 5 * JK
30 = 5 * JK
Next, we isolate JK by dividing both sides of the equation by 5:
30 / 5 = JK
6 = JK
Therefore, the length of JK is 6.