Find x in terms of y
e-zgeometry. com/pow/pictures/25.gif
It would be helpful if the verticies had letters at the site you left:
http://www.e-zgeometry.com/pow/pictures/25.gif
The two smaller triangles are similar to the larger one (the altitude y)
To find x in terms of y in the given geometry problem, we need to use the concept of similar triangles.
Let's label the vertices of the triangle in the image as follows:
- The larger triangle (base) vertices: A, B, and C
- The top smaller triangle vertices: C, D, and E
- The bottom smaller triangle vertices: C, F, and G
We can see that the altitude, which is represented by y, divides the larger triangle into two smaller triangles that are similar to each other and to the larger triangle.
To find x in terms of y, we can use the concept of corresponding sides of similar triangles. In this case, the sides of the smaller triangles are proportional to the sides of the larger triangle.
From the smaller triangle CDE, we can see that:
CD/y = DE/x or x = (DE * y) / CD
Similarly, from the smaller triangle CFG, we can see that:
CF/y = FG/x or x = (FG * y) / CF
Since both expressions represent x, we can set them equal to each other:
(DE * y) / CD = (FG * y) / CF
Now, substitute the values from the image into the equation:
(x * y) / 20 = (15 * y) / 12
To find x, we can cross-multiply and solve for x:
12(x * y) = 20(15 * y)
12xy = 300y
Divide both sides of the equation by 12y to isolate x:
x = 300y / (12y)
x = 25
Therefore, the value of x in terms of y is x = 25.