Final answer:
To find the value of x that will make both triangles similar, set up a proportion comparing the corresponding sides of the triangles. Solve for x to determine the value that will make the triangles similar. In this case, x is approximately 8.33 inches.
Step-by-step explanation:
To find the value of x that will make both triangles similar, we need to compare the ratios of their corresponding sides. In a similar triangle, the ratio of the lengths of the corresponding sides will be the same.
Let's compare the base and height of the small triangle to the base and height of the larger triangle:
For the small triangle: base = x, height = 5 inches
For the large triangle: base = 7.5 inches, height = 4.5 inches
We can set up the following proportion:
x/5 = 7.5/4.5
Cross multiplying, we get:
4.5x = 5 * 7.5
Dividing both sides by 4.5, we find:
x = (5 * 7.5) / 4.5
Simplifying, we get:
x = 37.5 / 4.5
x ≈ 8.33 inches