SOLUTION: If the area of this rectangle is 105cm2 then the length is ____cm, the width is ____ cm, and the perimeter is ____cm. The width of the rectangle is (x) and the length is (2x+1). Th
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Question 68680: If the area of this rectangle is 105cm2 then the length is ____cm, the width is ____ cm, and the perimeter is ____cm. The width of the rectangle is (x) and the length is (2x+1). This is all the information the problem gives me. The problem was given to me on a study guide along with the answer key. The length is 15cm, and the width is 7 but I dont understand how they came about this answer. Can you please help me??
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Starting with the formula for the area of a rectangle: which is given as 105 sq.cm., you can substitute x for W and (2x+1) for L to get:
Simplify and solve for x.
Subtract 105 from both sides of the equation.
Factor this quadratic equation.
Apply the zero product principle.
and/or from which you get:
Subtract 15 from both sides.
} Divide both sides by 2.
Discard this negative solution as the width must be a positive value.
The width is 7 cm.
The length is 2x+1 = 2(7)+1 = 15 cm.
The perimeter is:
cm.
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