MATH SOLVE

5 months ago

Q:
# a rectangle is 4 centimeters longer than it is wide. the area is 117 square centimeters. find the dimensions of the rectangle

Accepted Solution

A:

Answer:width: 9 cmlength: 13 cmStep-by-step explanation:Integer factors of 117 include ...... 117 = 1×117 = 3×39 ≈ 9×13The last factor pair is two factors that differ by 4. We can take these to be the dimensions of the rectangle._____If you want to write an equation for width (w), it might be ...... w(w+4) = 117... w² +4w -117 = 0The factorization problem for this quadratic is the problem of finding two factors of 117 that differ by 4. That is what we have done, above.If you want to solve this by completing the square, you can to this:... w² +4w = 117... w² +4w +4 = 121 . . . . . add 4 = (4/2)² to complete the square... (w+2)² = 121... w + 2 = ±√121 = ±11 . . . . take the square root... w = -2 ± 11 . . . . . we're only interested in the positive solution... w = 9, then w+4 = 13 and the dimensions are 9 cm by 13 cm.