ABC is similar to DEC. Find the length of x. AB=11.25 DE= 1.25 EC= 2.7 and x =BC. I have no clue . Frustrated!
Triangle abc is similar to triangle def.
Find the perimeter of def
To find the length of x (BC), we can use the concept of similar triangles.
In similar triangles, corresponding sides are proportional.
Given:
AB = 11.25
DE = 1.25
EC = 2.7
Since ABC is similar to DEC, we can write the following proportion:
AB/DE = BC/EC
Substituting the given values:
11.25/1.25 = x/2.7
To find x, we can cross multiply and solve for x:
11.25 * 2.7 = 1.25 * x
30.375 = 1.25x
Dividing both sides by 1.25, we get:
x = 30.375 / 1.25
x = 24.3
Therefore, the length of x (BC) is 24.3.
To find the length of x, we need to use the property of similar triangles. Similar triangles have the same shape but possibly different sizes. In this case, we have triangle ABC and triangle DEC, which are similar.
In similar triangles, corresponding sides are proportional. This means that if we take the ratio of any pair of corresponding sides, it will be the same for all pairs of corresponding sides.
Let's identify the corresponding sides of triangles ABC and DEC:
- AB corresponds to DE
- BC corresponds to EC
- AC corresponds to DC
Given the lengths of AB, DE, EC, and the fact that x is the length of BC, we can set up a proportion to find x.
The proportion for similar triangles ABC and DEC is: AB/DE = BC/EC
Plugging in the known values, we have: 11.25/1.25 = x/2.7
To solve for x, we can cross-multiply:
11.25 * 2.7 = 1.25 * x
Simplifying, we get:
30.375 = 1.25x
Dividing both sides by 1.25, we find:
x = 30.375 / 1.25
Calculating this, we get:
x ≈ 24.3
Therefore, the length of x, or BC, is approximately 24.3 units.
Simple!
You must have learned that for similar triangles the corresponding sides are in the same ratio, so
x/11.25 = 2.7/1.25
x = (2.7/1.25)(11.25) = 24.3