The length and width of the similar rectangular screen are 110 meters and 35 meters respectively.
<u>SOLUTION:
</u>
Given, A huge suspended LED screen is the centerpiece of The Place, a popular mall in Beijing, China.
We have to find the length and width of a similar rectangular screen
We are also given that the length is 5 meters more than 3 times its width,
Let width of rectangle be "b" meters, the its length will be 5 + 3b meters
And, the viewable area is 3,850 square meters.
![\begin{array}{l}{\text { So, area }=3850} \\\\ {\text { Length } \times \text { width }=3850} \\\\ {(5+3 b) \times b=3850} \\\\ {5 b+3 b^{2}=3850} \\\\ {3 b^{2}+5 b-3850=0}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5Ctext%20%7B%20So%2C%20area%20%7D%3D3850%7D%20%5C%5C%5C%5C%20%7B%5Ctext%20%7B%20Length%20%7D%20%5Ctimes%20%5Ctext%20%7B%20width%20%7D%3D3850%7D%20%5C%5C%5C%5C%20%7B%285%2B3%20b%29%20%5Ctimes%20b%3D3850%7D%20%5C%5C%5C%5C%20%7B5%20b%2B3%20b%5E%7B2%7D%3D3850%7D%20%5C%5C%5C%5C%20%7B3%20b%5E%7B2%7D%2B5%20b-3850%3D0%7D%5Cend%7Barray%7D)
Now,let us use quadratic formula:
![\begin{array}{l}{\mathrm{x}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}} \\\\ {\text { Then, } \mathrm{b}=\frac{-5 \pm \sqrt{5^{2}-4 \times 3 \times(-3850)}}{2 \times 3}}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5Cmathrm%7Bx%7D%3D%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E%7B2%7D-4%20a%20c%7D%7D%7B2%20a%7D%7D%20%5C%5C%5C%5C%20%7B%5Ctext%20%7B%20Then%2C%20%7D%20%5Cmathrm%7Bb%7D%3D%5Cfrac%7B-5%20%5Cpm%20%5Csqrt%7B5%5E%7B2%7D-4%20%5Ctimes%203%20%5Ctimes%28-3850%29%7D%7D%7B2%20%5Ctimes%203%7D%7D%5Cend%7Barray%7D)
![\begin{array}{l}{\mathrm{b}=\frac{-5 \pm \sqrt{25+46200}}{6}} \\\\ {\mathrm{b}=\frac{-5 \pm \sqrt{46225}}{6}} \\\\ {\mathrm{b}=\frac{-5 \pm 215}{6}} \\\\ {\mathrm{b}=\frac{-5+215}{6} \text { or } \frac{-5-215}{6}} \\\\ {\mathrm{b}=\frac{210}{6} \mathrm{or} \frac{-220}{6}}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5Cmathrm%7Bb%7D%3D%5Cfrac%7B-5%20%5Cpm%20%5Csqrt%7B25%2B46200%7D%7D%7B6%7D%7D%20%5C%5C%5C%5C%20%7B%5Cmathrm%7Bb%7D%3D%5Cfrac%7B-5%20%5Cpm%20%5Csqrt%7B46225%7D%7D%7B6%7D%7D%20%5C%5C%5C%5C%20%7B%5Cmathrm%7Bb%7D%3D%5Cfrac%7B-5%20%5Cpm%20215%7D%7B6%7D%7D%20%5C%5C%5C%5C%20%7B%5Cmathrm%7Bb%7D%3D%5Cfrac%7B-5%2B215%7D%7B6%7D%20%5Ctext%20%7B%20or%20%7D%20%5Cfrac%7B-5-215%7D%7B6%7D%7D%20%5C%5C%5C%5C%20%7B%5Cmathrm%7Bb%7D%3D%5Cfrac%7B210%7D%7B6%7D%20%5Cmathrm%7Bor%7D%20%5Cfrac%7B-220%7D%7B6%7D%7D%5Cend%7Barray%7D)
Neglect negative values as width can’t be negative
![b=\frac{210}{6}=35](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B210%7D%7B6%7D%3D35)
so, width = 35 meters, then length = 5 + 3(35) = 5 + 105 = 110 meters
hence, the length and width of the similar rectangular screen are 110 meters and 35 meters respectively.