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AssignmentMultiple Select

Solving Quadratic Equations: Factoring

Question 10 • FL-1200700-Mathematics for College Algebra MIS

A rectangular piece of paper has a width that is 3 inches less than its length. It is cut in half along a diagonal to create two congruent right triangles with areas of 44 square inches. Which statements are true? Check all that apply.The area of the rectangle is 88 square inches.The equation x(x – 3) = 44 can be used to solve for the dimensions of the triangle.The equation x2 – 3x – 88 = 0 can be used to solve for the length of the rectangle.The triangle has a base of 11 inches and a height of 8 inches.The rectangle has a width of 4 inches.

Answer
A
The area of the rectangle is 88 square inches.
B
The equation x(x – 3) = 44 can be used to solve for the dimensions of the triangle.
C
The equation x2 – 3x – 88 = 0 can be used to solve for the length of the rectangle.
D
The triangle has a base of 11 inches and a height of 8 inches.
E
The rectangle has a width of 4 inches.

Explanation

The rectangle is made of two congruent triangles, each with area 44 square inches, so its area is 2 × 44 = 88 square inches. If its length is x, its width is x − 3, so x(x − 3) = 88, or x² − 3x − 88 = 0; this makes statement C true and statement B false. Factoring gives (x − 11)(x + 8) = 0, so the length is 11 inches and the width is 8 inches. Thus the triangle’s base and height can be 11 inches and 8 inches, and the width is not 4 inches.

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