Question

The rectangular poster shown at the right measures 2w-30. The poster has an area of 5400 cm squared. What is the value of w?

Answer 1

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:

$Area = length \times width\\\\5400 = (2w - 30) \times w\\\\5400 = 2w^2 - 30w\\\\2w^2 - 30w - 5400 = 0$

Solve by quadratic formula

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=2,\:b=-30,\:c=-5400$

$w = \frac{-\left(-30\right)\pm \sqrt{\left(-30\right)^2-4\cdot \:2\left(-5400\right)}}{2\cdot \:2}$

$w = \frac{ 30 \pm \sqrt{44100}}{4}\\\\w = \frac{ 30 \pm 210 }{4}$

We have two solutions

$w = \frac{30+210}{4}\\\\w = 60\\\\And\\\\w = \frac{30-210}{4}\\\\w=-45$

Ignore, negative value as width cannot be negative

Thus value of w is 60