Question

A bricklayer will put cement on the floor of my patio that has a rectangular shape of 15 m long and whose perimeter is less than 50 m. What is the maximum integer value that the width of my patio could have?

A. 7

B. 10

C. 12

D. 25

Answer 1

Using the formula for the perimeter of a rectangle and setting up the inequality based on the given information, the maximum integer width that satisfies the condition is 9. Given the options, the largest integer less than 10 and available in the choices is 7.

Step-by-step explanation:

To find the maximum integer value for the width that the bricklayer can have for a rectangular patio that is 15 m long with a perimeter of less than 50 m, we can use the formula for the perimeter of a rectangle, P = 2l + 2w, where l is the length and w is the width of the rectangle.

Since we know the length (l) is 15 m and the perimeter (P) is less than 50 m, we can set up the inequality: 2(15) + 2w < 50. Simplifying, we get 30 + 2w < 50, which results in 2w < 20 after subtracting 30 from both sides. Dividing by 2 to solve for w, we find that w < 10.

The maximum integer value for the width is the largest whole number less than 10, which is 9. However, this option is not listed among the choices provided. Among the given choices, the largest integer that is less than 10 is 7. Therefore, the correct answer to the question is A. 7.