Question

Mika will use copies of one of the triangles shown in the diagram below to cover a rectangular poster as completely as possible.

The poster is 12 inches wide and has an area of 480 square inches. The triangle Mika will use is isosceles. The copies are all full size and do not overlap on the poster. Which set of statements identify the triangle Mika should use to cover the poster as completely as possible and the area of the poster that will remain uncovered?

A
Mika should use triangle 1, and no portion of the poster will remain uncovered.

B
Mika should use triangle 2, and no portion of the poster will remain uncovered.

C
Mika should use triangle 3, and 48 square inches of the poster will remain uncovered.

D
Mika should use triangle 3, and 12 square inches of the poster will remain uncovered.

Answer 1

Answer: The correct answer is choice C.

If the area of the poster is 480 square inches and the width is 12, then the length must be 40.

If Mika uses triangle number 3, she can put them together to form a 6 by 6 square. Two of these square will fit along the width because it is 12 inches wide.

She could stack 6 of them on top of each other and that would reach 36 inches tall.

Thus leaving 4 inch rows of 12 inches, or 4 x 12 = 48 inches uncovered.