Triangle ABC is similar to triangle DEF. The sides of ABC are 5,8 and 11. What is the length of the shorttest side of DEF if its perimeter is 60?
Since the sides must be in the same ratio...
let the sides of the new triangle be
5x, 8x, and 11x
5x + 8x + 11x = 80
solve for x, then find 5x
5x + 8x + 11x = 60 , hit the wrong key
12.5
mc069-1.jpg
In mc069-2.jpg, FE = 13 and mc069-3.jpg. Find DF to the nearest tenth.
To find the length of the shortest side of triangle DEF, we first need to determine the scale factor between triangles ABC and DEF. Since the corresponding sides of similar triangles are in proportion, we can set up a proportion using the lengths of the corresponding sides.
In triangle ABC, the sides are 5, 8, and 11. Let's label the sides of triangle DEF as x, y, and z. Since we want to find the length of the shortest side, we can assign x to be the shortest side of triangle DEF.
Setting up the proportion:
5/8 = x/y
Now, let's calculate the scale factor:
5/8 = x/y
5y = 8x
y = (8/5)x
Now that we have the relationship between the sides of triangle DEF, we can calculate the lengths of the sides. We are given the perimeter of triangle DEF, which is 60. The perimeter is the sum of all the sides.
x + y + z = 60
Substituting the value of y:
x + (8/5)x + z = 60
(13/5)x + z = 60
Since we want to find the length of the shortest side, we know that x will be the smallest value among x, y, and z. Thus, we can assume z will be the largest value. Therefore, let's assign the remaining side z as the longest side, z = 2x.
Now we have the following two equations:
(13/5)x + 2x = 60
(33/5)x = 60
To find x, we can solve for x by multiplying both sides by (5/33):
x = (60 * 5) / 33
x ≈ 9.09
Since we rounded x to two decimal places, we'll round z accordingly:
z = 2x ≈ 2 * 9.09 ≈ 18.18
Now we have the lengths of the sides x and z. The shortest side of triangle DEF is x, which is approximately 9.09 units in length.