Question

the length of a rectangle is 1 cm more than twice it's width. of area of the rectangle is 21 cm^2 then what are the dimensions?

Answer 1

You are given a rectangle and are told that the length is 1 cm more than twice the width of the rectangle.  The area of the rect. is also given, and is 21 cm^2.

Find the length and width.  To do this, represent the length by y and the width by x.  Then "1 cm more than twice the width" comes out to y=2x+1 (cm).

Since the area of a rect. is equal to the product of its length and width, 

x(2x+1)=21 cm^2.  Multiply out x(2x+1).  show your work.  Next, subtract 21 from both sides.  Write your algebraic expression on the left side as a quadratic equation in standard form.

Solve this quadratic equation for x.  Recall that x (in cm) will represent the width of the rect., and y=2x+1 (in cm) will repr. the length.