Question

The length of a rectangle is 6 more than the width. The area is 720 square feet. Find the length and width of the rectangle.

Answer 1

Given :-

• The length of a rectangle is 6 more than the width

• Area of rectangle = 720 feet²

To find:-

• Length
• Width

Let :-

• Width of rectangle = x
• Length of rectangle = 6 + x

Solution:-

So to find length and width of rectangle, we have to find value of x.

We know:-

$\bigstar \boxed{ \rm Area~of~rectangle=Length\times{}Width}$

By using this formula we can find value of x.

So:-

$\dashrightarrow\sf Area~of~rectangle=Length\times{}Width$

$\dashrightarrow\sf 720=(x + 6)(x)$

$\dashrightarrow\sf 720=x(x) +x( 6)$

$\dashrightarrow\sf 720= {x}^{2} +x( 6)$

$\dashrightarrow\sf 720= {x}^{2} +6x$

$\dashrightarrow\sf0 = {x}^{2} +6x - 720$

$\dashrightarrow\sf {x}^{2} +6x - 720 = 0$

$\dashrightarrow\sf {x}^{2} +30x - 24x - 720 = 0$

$\dashrightarrow\sf ({x}^{2} +30x )- 24x - 720 = 0$

$\dashrightarrow\sf x({x}+30 )- 24x - 720 = 0$

$\dashrightarrow\sf x({x}+30 ) + (- 24x - 720) = 0$

$\dashrightarrow\sf x({x}+30 ) - 24(x+ 30) = 0$

$\dashrightarrow\sf (x - 24)({x}+30 )= 0$

We got two solutions:-

first solution

• x - 24 = 0
• x = 24

Second solution :-

• x + 30 = 0
• x = -30

Length can't be taken negative so 24 is the value of x.

Value of width:-

• Width of rectangle = x
• Width = 24 feet

Value of Length:-

• Length of rectangle = x + 6
• Length = 24 + 6
• Length = 30 feet