APPLICATIONS OF PROPORTIONS WORKSHEET

Problem 1 :

In the diagram shown below ΔRST ∼ ΔBCD. Find the length of BC.

Problem 2 :

In the diagram shown below FGHJKL ∼ MNPQRS. Find the length of QR.

Problem 3 :

In the diagram shown below ABCD ∼ WXYZ. Find the length of XY.

Problem 4 :

A totem pole casts a shadow 45 feet long at the same time that a 6-foot-tall man casts a shadow that is 3 feet long. Write and solve a proportion to find the height of the totem pole.

Problem 5 :

Every dimension of a 2-by-4-inch rectangle is multiplied by 1.5 to form a similar rectangle. How is the ratio of the perimeters related to the ratio of corresponding sides? How is the ratio of the areas related to the ratio of corresponding sides?

Problem 6 :

Every dimension of a cylinder with radius 4 cm and height 6 cm is multiplied by ½ to form a similar cylinder. How is the ratio of the volumes related to the ratio of corresponding dimensions?

1. Answer :

R corresponds to B, S corresponds to C, and T corresponds to D.

RT/BD = RS/BC

5/12 = 8/x

Use Cross Product Property.

5(x) = 12(8)

5x = 96

Because x is multiplied by 5, divide each side by 5 to undo the multiplication.

5x/5 = 96/5

x = 19.2

The length of BC is 19.2 ft.

2. Answer :

GH/NP = JK/QR

4/6 = 2/x

Use Cross Product Property.

4(x) = 6(2)

4x = 12

Because x is multiplied by 4, divide each side by 4 to undo the multiplication.

4x/4 = 12/4

x = 3

The length of QR is 3 cm.

3. Answer :

AB/WX = BC/XY

5/7 = 2/x

Use Cross Product Property.

5(x) = 7(2)

5x = 14

Because x is multiplied by 5, divide each side by 5 to undo the multiplication.

5x/5 = 14/5

x = 2.8

The length of XY is 2.8 cm.

4. Answer :

Both the man and the totem pole form right angles with the ground, and their shadows are cast at the same angle. You can form two similar right triangles.