Respuesta :
Complete Question:
The rectangular poster shown measures 2w-30 by w. The poster has an area of 5400 cm2. What is the value of w?
Answer:
The value of w is 60
Solution:
Given that,
The rectangular poster shown measures 2w-30 by w
Area = 5400 square centimeter
The area of rectangle is given as:
[tex]Area = length \times width\\\\5400 = (2w - 30) \times w\\\\5400 = 2w^2 - 30w\\\\2w^2 - 30w - 5400 = 0[/tex]
Solve by quadratic formula
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:}\quad a=2,\:b=-30,\:c=-5400[/tex]
[tex]w = \frac{-\left(-30\right)\pm \sqrt{\left(-30\right)^2-4\cdot \:2\left(-5400\right)}}{2\cdot \:2}[/tex]
[tex]w = \frac{ 30 \pm \sqrt{44100}}{4}\\\\w = \frac{ 30 \pm 210 }{4}[/tex]
We have two solutions
[tex]w = \frac{30+210}{4}\\\\w = 60\\\\And\\\\w = \frac{30-210}{4}\\\\w=-45[/tex]
Ignore, negative value as width cannot be negative
Thus value of w is 60
