Question

A rectangle has a length of 13 yards less than 10 times it’s width. If the area of the rectangle is 13946 square yards, find the length of the rectangle.

Answer 1

367 yards

Explanation:

If we let x and y represent the length and width, respectively, then the problem statement can be translated to ...

x = 10y -13

xy = 13946

Substituting the first equation into the second gives ...

(10y -13)y = 13946

10y^2 -13y -13946 = 0 . . . . rearranged to standard form

Using the quadratic formula

x = (-b±√(b^2-4ac))/(2a) . . . gives the solutions to ax^2 +bx +c = 0

we can find the positive value of y to be

y = (-(-13) +√((-13)^2 -4(10)(-13946)))/(2·10) = (13 +√558009)/20

y = 38

The corresponding value of x is ...

x = 10·38 -13 = 367

The length of the rectangle is 367 yards.