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:

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

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

$x=\frac{-5 \pm \sqrt{2105}}{4}$

$x=\frac{-5+\sqrt{2105}}{4}, \ x=\frac{-5-\sqrt{2105}}{4}$

x = 10.22,   x = –12.72006

Dimension of the figure cannot be measured in negative terms.

Hence x = 10.22 in.