Question

What are the diameters of the painting?
Easy!!!

Answer 1

x = 10.22 in

Solution:

Width of the figure = x in

Length of the figure = (2x + 5) in

Area of the figure = 260 in²

To find the value of x:

Area of the figure = length × width

length × width = 260

(2x + 5) × x = 260

`2x^2+5x=260`

Subtract 260 from both sides of the equation.

`2x^2+5x-260=0`

Factor the above quadratic expression.

Quadratic equation formula:

`$x=\frac{-b \pm \sqrt{b^(2)-4 a c}}{2 a}`

`$x=\frac{-5 \pm \sqrt{5^(2)-4 \cdot 2(-260)}}{2 \cdot 2}`

`$x=(-5 \pm √(2105))/(4)`

`$x=(-5+√(2105))/(4), \ x=(-5-√(2105))/(4)`

x = 10.22, x = –12.72006

Dimension of the figure cannot be measured in negative terms.

Hence x = 10.22 in.