91Ó°ÊÓ

Suppose that the width of a certain rectangle is 3 inches less than its length. The area is numerically 6 less than twice the perimeter. Find the length and width of the rectangle.

For Problems \(47-60\), use the process of factoring by grouping to factor each polynomial. (Objective 3 ) $$ 6 n^{2}-3 n-8 n+4 $$

$$ \text { For Problems 45-68, solve each equation. (Objective 2) } $$ $$ n^{3}=16 n $$

$$ \text { For Problems 51-80, solve each equation. (Objective 2) } $$ $$ 6 t^{2}+37 t-35=0 $$

The sum of the areas of a square and a rectangle is 64 square centimeters. The length of the rectangle is 4 centimeters more than a side of the square, and the width of the rectangle is 2 centimeters more than a side of the square. Find the dimensions of the square and the rectangle.

For Problems \(47-60\), use the process of factoring by grouping to factor each polynomial. (Objective 3 ) $$ 20 n^{2}+8 n-15 n-6 $$

$$ \text { For Problems } 41-70 \text {, solve each equation. (Objective } 3 \text { ) } $$ $$ n^{2}+33 n+270=0 $$

$$ \text { For Problems 51-80, solve each equation. (Objective 2) } $$ $$ 2 t^{2}+15 t-27=0 $$

$$ \text { For Problems 45-68, solve each equation. (Objective 2) } $$ $$ 2 n^{3}=8 n $$

The perimeter of a rectangle is 30 centimeters, and the area is 54 square centimeters. Find the length and width of the rectangle. [Hint: Let \(w\) represent the width; then 15 - \(w\) represents the length.]