A wall 10 ft high along the property line is 8 ft from a house. A ladder was placed in such a way that the other end will reach the house and the other end rests on the ground outside the wall. Find the length of the shortest ladder that will reach the house.
| A. 32.6 ft | C. 25.4 ft |
| B. 22.3 ft | D. 28.8 ft |
A triangle has a variable sides x, y, and z subject to the constraint that the perimeter P is fixed to 18 cm. What is the maximum possible area of the triangle?
| A. 18.81 cm2 | C. 17.78 cm2 |
| B. 16.62 cm2 | D. 15.59 cm2 |
A corner lot, triangular in shape, has perpendicular sides measuring 90 m and 120 m, respectively. It is required to construct the largest rectangular building with sides parallel to the longest side. What is the largest area of the building in square meter?
| A. 2400 | C. 2500 |
| B. 2700 | D. 2600 |
If 1200 cm2 of material is available to make a box with a square base and open top, find the largest possible volume of the box.
| A. 4000 cc | C. 2000 cc |
| B. 3000 cc | D. 2500 cc |
A closed cylindrical tank having a volume of 71.57 m3 is to be constructed. If the surface area is to be minimum, what is the required diameter of the tank?
| A. 4 m | C. 5 m |
| B. 5.5 m | D. 4.5 m |
Two vertices of a rectangle are on the positive x-axis. The other two vertices are on the lines y = 4x and y = 6 - 5x. What is the maximum possible area of the rectangle?
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus, the diameter of semicircle is equal to the width of the rectangle.) If the perimeter of the window is 30 ft, find the width of the window so that the greatest possible amount of light is admitted.
| A. 4.2 ft | C. 10.6 ft |
| B. 8.4 ft | D. 5.3 ft |
A cylindrical can is to be made to hold 1 liter of oil. Find the radius that will minimize the cost of the metal to manufacture the can.
| A. 4.52 cm | C. 9.04 cm |
| B. 5.42 cm | D. 10.84 cm |
A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area?
| A. 600 ft wide along the river × 900 ft deep | C. 700 ft wide along the river × 850 ft deep |
| B. 1200 ft wide along the river × 600 ft deep | D. 1000 ft wide along the river × 700 ft deep |
Find the area of the largest rectangle that can be inscribed in a right triangle with legs of length 3 cm and 4 cm if two sides of the rectangle lie along the legs.
| A. 6 cm2 | C. 4 cm2 |
| B. 5 cm2 | D. 3 cm2 |
