Since the ratio of corresponding sides in similar triangles is equal, we have the proportion: (y + 5) / 10 = 5 / 10. Solving for y, we get y = 20.
To solve for y in the given image using the concept of proportionality, we can use the following steps:
Identify the two similar triangles.
In the image, the two similar triangles are triangle JHI and triangle GFI.
Write down the proportion of corresponding sides in the two triangles.
Since the triangles are similar, the ratio of corresponding sides is equal.
Therefore, we have the following proportion:
(HI + y) / FI = y / GI
Solve for y.
We can solve for y by cross-multiplying and simplifying:
(HI + y) * GI = y * FI
HI * GI + y * GI = y * FI
y * (GI - FI) = HI * GI
y = HI * GI / (GI - FI)
Substituting the values from the image, we get:
y = 5 * 10 / (10 - 5)
y = 5 * 10 / 5
y = 20
Therefore, the value of y is 20.