A quadrilaterals smallest side measures 29 mm and it's largest side measures 38 mm. A similar quadrilaterals largest side measures 95 mm. What is the measure of its smallest side?
To find the measure of the smallest side of the similar quadrilateral, you can set up a proportion using the ratios of the corresponding sides.
Let's assume the measure of the smallest side of the similar quadrilateral is x mm.
The ratio of the largest sides of the quadrilaterals is:
38 mm / 95 mm
The ratio of the smallest sides of the quadrilaterals is:
29 mm / x mm
Setting up the proportion:
38 mm / 95 mm = 29 mm / x mm
Cross-multiplying, we get:
38 mm * x mm = 29 mm * 95 mm
Simplifying:
38x = 2755
Dividing both sides by 38:
x = 2755 / 38
Calculating:
x ≈ 72.5 mm
Therefore, the measure of the smallest side of the similar quadrilateral is approximately 72.5 mm.
Let's assume the scale factor between the two similar quadrilaterals is represented by "k".
From the given information, we know that the smallest side of the first quadrilateral measures 29 mm and the largest side measures 38 mm. So, in terms of the scale factor "k", we can say:
k * 29 mm = smallest side of the second quadrilateral
k * 38 mm = largest side of the second quadrilateral
We are also given that the largest side of the second quadrilateral measures 95 mm. So, we can set up the equation:
k * 38 mm = 95 mm
Now, we can solve for "k":
k = 95 mm / 38 mm
k ≈ 2.5
Now, we can find the measure of the smallest side of the second quadrilateral:
k * 29 mm = 2.5 * 29 mm
≈ 72.5 mm
Therefore, the measure of the smallest side of the second quadrilateral is approximately 72.5 mm.