Question

The length of a rectangle is 1 ft less than twice the width, the area of the rectangle is 21 ft squared. What’s the length

Answer 1

Answer:

The length of the rectangle is 6 feet

Step-by-step explanation:

Given as :

The length of rectangle is 1 feet less than twice the width

So, let The width of rectangle = w feet

The length of rectangle = ( 2 w - 1 )  feet

The area of the rectangle = 21 feet²

Now,

∵ The area of the rectangle = length × width

Or, 21 feet² =  ( 2 w - 1 ) feet × w feet

or, 21 = 2 w² - w

or, 2 w² - w - 21 = 0

or, 2 w² + 6 w - 7 w - 21 = 0

or , 2 w ( w + 3 ) - 7 ( w + 3 ) = 0

or, ( w + 3 ) ( 2 w - 7 ) = 0

So, w = - 3 feet , $\frac{7}{2}$ feet

here we consider only positive value of w i.e  $\frac{7}{2}$ feet

∴ The length of rectangle = ( 2 w - 1 )  feet

or,  The length of rectangle = 2 × $\frac{7}{2}$  - 1

Or, The length of rectangle = 7 - 1 = 6 feet

Hence The length of the rectangle is 6 feet , Answer