Question

A huge suspended LED screen is the centerpiece of The Place, a popular mall in Beijing, China. Find the length and width of a similar rectangular screen if the length is 5 meters more than 3 times its width, and the viewable area is 3,850 square meters.

Answer 1

Answer:

$Lenght=110\ m\\Width=35\ m$

Step-by-step explanation:

The area of a rectangle can be calculated with this formula:

$A=lw$

Where "l" is the lenght and "w" is the width.

In this case,based on the data given in the exercise, we know that:

$l=3w+5\\\\A=3,850$

Then, we can make the substitution into the formula $A=lw$:

$3,850=(3w+5)w$

Simplifying:

$3w^2+5w-3,850=0$

Now we can apply the Quadratic formula $w=\frac{-b\±\sqrt{b^2-4ac}}{2a}$.

In this case:

$a=3\\b=5\\c=-3,850$

Substituting these values into the formula, we get:

$w=\frac{-5\±\sqrt{5^2-4(3)(-3,850}}{2(3)}\\\\\\w_1=-36.66\\\\w_2=35}$

Since the width cannot be negative:

$w=35\ m$

Substituting the width into $l=3w+5$, we get:

$l=3(35)+5\\\\l=110\ m$