Question

A tapestry in the Louvre museum is for sale and has a width of x feet and length that is 8 feet less than it's width. An art collector will only purchase the tapestry if it measures 240 square feet in area. What value for x causes the art collector to purchase the tapestry. show work

Answer 1

First draw a rectangle

width = x ft

Length = x - 8 ft

Area = 240 square feet

Area = Length X width

240 = x(x - 8)

`\begin{gathered} 240=x^2\text{ - 8x} \\ x^2\text{ - 8x - 240 = 0} \\ \text{Factorize the equation } \\ x^2\text{ - }20x\text{ + 12x -240 = 0} \\ x(x\text{ - 20) + 12(x - 20) = 0} \\ (x\text{ - 20)(x + 12) = 0} \\ x\text{ - 20 = 0 or x + 12 = 0} \\ x\text{ = 20} \end{gathered}`