Question

A building in a city has a rectangular base. The length of the base measures 75 ft less than three times the width. The perimeter of this base is 810 ft. What are the dimensions of the​ base?

Answer 1

The answer to your problem is Length=275ft, and Width=175ft.

Explanation:

Perimeter= 2*(Length + Width) = 900ft

and Length = 2*Width - 75ft

Then by substituting the length for its equivalent in terms of the width, we have:

Perimeter=2*(2*Width - 75ft + Width) = 2*(3*Width - 75ft) = 6*Width - 150ft

Then equating this equation to P=900ft, we have:

6*Width - 150ft = 900ft

6*Width = 900ft + 150ft = 1050 ft

Width = 1050 ft / 6 = 175 ft

And from there, calculate length from width:

Length = 2*(175ft) - 75ft = 275 ft.

Final check, Perimeter = 2*(Length + Width) = 2*(275ft + 175ft) = 900ft.