✭ Question -:
A rectangle has a length of (2x+1) units, a width of (x-7) units and an Area of 17 square units. Find the dimensions of the rectangle.
✭ Explanation -:
In this question we are provided with the length of a rectangle (2x + 1) units and the width of the rectangle (x - 7). It is also given that the area is 17 units². We are asked to calculate the length and width of the rectangle.
First we will find the value of x
We know,
[tex] \bull \: \small\boxed{ \rm{ Area_{(rectangle)} = Length × Width}}[/tex]
Substituting the values we get
[tex] \small\sf{ (2x + 1 ) (x - 7) = 17}[/tex]
[tex] \small\rm{ 2x( x - 7) + 1(x - 7) = 17}[/tex]
[tex] \small\rm{ 2 {x}^{2} - 14x + 1(x - 7) = 17}[/tex]
[tex] \small\rm{ 2 {x}^{2} - 13x - 7 = 17}[/tex]
[tex] \small\rm{2 {x}^{2} - 13x - 7 - 17 = 0 } [/tex]
[tex] \small\rm{2 {x}^{2} - 13x - 24 = 0} [/tex]
[tex] \small\rm{x = \dfrac{13 + 19}{2 \times 2} } [/tex]
[tex] \small\rm{ x = \dfrac{32}{4} = 8}[/tex]
[tex] \small\sf{x = 8} [/tex]
Now we will substitute the value of x
Length = (2x + 1) = 2 × 8 + 1 = 16 + 1 = 17 units
Width = (x - 7) = 8 - 7 = 1 units
- Hence, the length of the rectangle is 17 units and the width is 1 units.
