Arectangle 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.

  367 yards

Step-by-step 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.

5 cm

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32

2(10 - 13x) + 9x = -34x + 6020 - 26x + 9x = -34x + distributive property-17x = -34x + subtraction property (subtracted 20 from both sides)17x = addition property (added 34x to both sides)x = 40/ division property (divided both sides by 17)