Question

A rectangular coffee table has an area given by the trinomial m^2 + 10m + 24.

a. What are the dimensions of the table in terms of 'm'?
b. Calculate the perimeter of the table in terms of 'm.'
c. If the value of 'm' is equal to 5, what would be the area of the table?"

Answer 1

a. The dimensions of the table are (m + 4) and (m + 6). b. The perimeter of the table in terms of 'm' is 4m + 20. c. If 'm' is equal to 5, the area of the table is 99.

Step-by-step explanation:

a. To find the dimensions of the table, we need to factor the trinomial m^2 + 10m + 24. The factors of the trinomial are (m + 4)(m + 6). Therefore, the dimensions of the table are (m + 4) and (m + 6).

b. The perimeter of a rectangle is given by the formula P = 2(l + w), where l and w are the length and width of the rectangle. In this case, the length is (m + 4) and the width is (m + 6). So, the perimeter of the table in terms of 'm' is equal to P = 2[(m + 4) + (m + 6)] = 2(2m + 10) = 4m + 20.

c. If the value of 'm' is equal to 5, we can substitute this value into the area formula to find the area of the table. A = (5 + 4)(5 + 6) = 9(11) = 99.