Final answer:
To find the base of the larger triangle, set up the proportion 6 inches / 8 inches = x inches / 6 inches, cross-multiply, and solve for x, resulting in x being 4.5 inches.
Step-by-step explanation:
Since the two triangles are similar, their corresponding sides are proportional. We are given the base and height of the smaller triangle (6 inches and 8 inches respectively) and the height of the larger triangle (6 inches). We are asked to find the base (x) of the larger triangle.
To solve for x, we set up a proportion using the sides of the smaller triangle and the corresponding sides of the larger triangle. The proportion is as follows:
Base of smaller triangle / Height of smaller triangle = Base of larger triangle (x) / Height of larger triangle
6 inches / 8 inches = x inches / 6 inches
Now, we cross-multiply to solve for x:
6 * 6 = 8 * x
36 = 8x
Divide both sides by 8 to isolate x:
x = 36 / 8
x = 4.5 inches
Therefore, the base of the larger triangle is 4.5 inches.