Question
Use the image to answer the question.
An illustration shows two triangles, one big and one small. In the big triangle, one side measures 13 yards and another side measures x. In the small triangle, the side corresponding to 13 yards in the big triangle measures 3.25 yards and the side corresponding to x measures 4.23 yards.
Use proportions to find the missing side length (x) in the two similar figures.
(1 point)
9.99 yards
16.92 yards
1.05 yards
4 yards
To find the missing side length (x) in the two similar figures, we can set up a proportion.
The proportion would be:
(13 yards / x) = (3.25 yards / 4.23 yards)
To solve for x, we can cross-multiply and then divide:
13 yards * 4.23 yards = x * 3.25 yards
55.29 yards = 3.25x
Divide both sides by 3.25:
x = 55.29 yards / 3.25
x ≈ 16.92 yards
Therefore, the missing side length (x) is approximately 16.92 yards.
The correct answer is 16.92 yards.
To find the value of x, we can set up a proportion using the corresponding side lengths of the two similar triangles.
In the big triangle, the ratio of the side lengths is x / 13.
In the small triangle, the ratio of the side lengths is 4.23 / 3.25.
Setting these two ratios equal to each other, we get:
x / 13 = 4.23 / 3.25
To solve for x, we cross-multiply and then divide:
x * 3.25 = 13 * 4.23
x * 3.25 = 55.99
Dividing both sides by 3.25, we get:
x = 55.99 / 3.25
x ≈ 17.2246
Rounding to two decimal places, the missing side length (x) is approximately 17.22 yards.