Question

The rectangular floor of the boardroom at DCR Industries has an area of 450 square feet. The width of the boardroom is 5 feet less than two thirds the length. Determine the length and width of the boardroom.

Answer 1

The boardroom is 25 feet long and 15 feet wide.

Step-by-step explanation:

Define variables:

Let L be the length of the boardroom.

Let W be the width of the boardroom.

Set up equations:

Area equation: L * W = 450 square feet

Width relation: W = (2/3)L - 5

Substitute the width relation into the area equation:

L * ((2/3)L - 5) = 450 square feet

Expand the parentheses: 2/3 L^2 - 5L - 450 = 0

Solve the quadratic equation:

Use the quadratic formula or factoring to find the solutions for L.

You will get two solutions; choose the one that makes sense in context (positive and realistic length).

Calculate the width using the chosen length:

W = (2/3)L - 5

Plug the chosen L value to find the corresponding W.

Therefore, the boardroom at DCR Industries is 25 feet long and 15 feet wide.

Answer 2

Answer:L = 30ft

W= 15ft

Step-by-step explanation:

l*w = 450

From the question

W = 2l/3 - 5

W = 450/l

450/l = (2l-15)/3

1350 = 2l^2 - 15l

2l^2 -15-1350 = 0

2l^2 +45l -60l- 1350 = 0

l(2l+45)- 30(2l+45)= 0

l-30 = 0 or 2l = 45

l= 30. or l = 22.5

w = 450/30 = 15. or w = 450/22.5= 20

Final answers are l = 30

w =15 since they are whole numbers