A quadrilateral’s smallest side measures 29mm and its largest measures 38mm. A similar quadrilateral’s largest side is 95mm. What is the measure of the smallest side?
To find the measure of the smallest side of the similar quadrilateral, we can set up a proportion using the ratios of the corresponding sides.
Let x be the measure of the smallest side of the similar quadrilateral.
The ratio of the smallest side to the largest side in the first quadrilateral is 29:38.
The ratio of the smallest side to the largest side in the second quadrilateral is x:95.
Setting up the proportion:
29/38 = x/95
Cross multiplying:
29 * 95 = 38 * x
2755 = 38x
Dividing by 38:
x = 72.5mm
Therefore, the measure of the smallest side of the similar quadrilateral is 72.5mm.
To find the lengths of the other two sides of the similar triangle, we need to determine the scale factor by comparing the corresponding sides of the two triangles.
Let the sides of the similar triangle be x and y, where x is the smallest side (1.4) and y is the unknown side length.
The scale factor between the two triangles is given by the ratio of the corresponding sides. The smallest side of the first triangle is 4.2, and the smallest side of the similar triangle is 1.4.
Scale factor = 1.4 / 4.2 = 0.3333 (rounded to 4 decimal places)
Now, we apply this scale factor to the other two sides of the original triangle:
4.2 * 0.3333 ≈ 1.4 (smallest side)
5.7 * 0.3333 ≈ 1.9
7.2 * 0.3333 ≈ 2.4
Therefore, the lengths of the other two sides of the similar triangle are approximately 1.9 and 2.4.