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# Word Problems Involving Geometric Shapes Practice Problems (page 2)

based on 1 rating
By McGraw-Hill Professional
Updated on Sep 27, 2011

#### Solutions

1. The area formula for a triangle is . The area is 12. The length of its base is two-thirds its height, so . The formula becomes .

The height of the triangle is 6 inches. Its base is inches.

2. The formula for the area of a triangle is . The area is 20. The height is 3 cm more than the base, so H = B + 3. The formula becomes .

The triangle’s base is 5 cm and its height is 5 + 3 = 8 cm.

3. The formula for the area of a triangle is . The area is 20. B + H = 14 so H = 14 – B . The formula becomes .

There are two triangles that satisfy the conditions. If the base is 10 inches, the height is 14 – 10 = 4 inches. If the base is 4 inches, the height is 14 – 4 = 10 inches.

4. By the Pythagorean theorem, a 2 + b 2 = c . The hypotenuse is c , so c = 85. One leg is 71 longer than the other so a = b + 71 ( b = a + 71 also works). The Pythagorean theorem becomes 85 2 = ( b + 71) 2 + b 2.

The shorter leg is 13 cm and the longer leg is 13 + 71 = 84 cm.

5. Because the can’s diameter is 6, the radius is 3. Let x represent the increase in the can’s radius. The radius of the new can is 3 + x. The volume of the current can is V = π r 2 h = π(3) 2 5 = 45π. To increase the volume by 50% means to add half of 45π to itself; the new volume would be . The volume formula for the new can becomes .

(The other solution is negative.)

The manufacturer should increase the can’s radius by about 0.674 inches. Because the diameter is twice the radius, the manufacturer should increase the can’s diameter by about 2(0.674) = 1.348 inches.

6. A pizza’s shape is circular so we need the area formula for a circle which is A = π r 2. The radius is half the diameter, so the restaurant’s large pizza has a radius of 8 inches. The area of the restaurant’s large pizza is π(8) 2 = 64π ≈ 201. The restaurant’s large pizza is 20% larger than the competition’s large pizza. Let A represent the area of the competition’s large pizza. Then 201 is 20% more than A :

The competition’s radius is approximately 7.3 inches, so its diameter is approximately 2(7.3) = 14.6 inches.

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