Question

Rickey has been commissioned to paint a mural that is allowed to have an area of 50 square meters. To make the rectangle shape of the mural easing to the eye, rickey wants the length to be five meters longer than twice its width. What lengths should rickey use fir the mural?

Answer 1

Answer:

12.808 meter is the length should Rickey use for the mural.

Step-by-step explanation:

Area of the mural = A = $50 m^2$

Length of the mural = l

Width of the mural = w

l = 5 + 2w

Area of the rectangle = l × w

$A=(5+2w)\times w$

$50 m^2=5w+2w^2$

$2w^2+5w-50=0$

Solving above equation with the help of Completing squares method:

$(\sqrt{2}w)^2+2\times \sqrt{2}w\times \frac{5}{2\sqrt{2}}+(\frac{5}{2\sqrt{2}})^2-50=(\frac{5}{2\sqrt{2}})^2$

$(a+b)^2=a^2+b^2+2ab$

$(\sqrt{2}w+\frac{5}{2\sqrt{2}})^2=(\frac{5}{2\sqrt{2}})^2+50$

$(\sqrt{2}w+\frac{5}{2\sqrt{2}})^2=\frac{25}{8}+50$

$(\sqrt{2}w+\frac{5}{2\sqrt{2}})^2=\frac{425}{8}$

$(\sqrt{2}w+\frac{5}{2\sqrt{2}})=\pm\sqrt{\frac{425}{8}}$

w = 3.904 m (accept)

w = -6.404 m (reject)

l = (5 + 2w)m = 5 + 2 × (3.904) m= 12.808 m

12.808 meter is the length should Rickey use for the mural.