Question

(iii) The length of the plot in meters is 1 more than twice its breadth and the area of a rectangle
plot is528m2. Which of the following quadratic equations represents the given situation:
(a) x2+2x - 528=0
(b) x2+x-528=0
(c) 2x2+x-528=0
(d)2x2 +x+ 528=0​

Answer 1

Answer :

Option (c) 2x² + x - 528 = 0

Step-by-step explanation :

Given,

• The length of the plot in meters is 1 more than twice its breadth
• The area of a rectangle  plot is 528m²

To find,

• The quadratic equation representing the given situation

Solution,

 Let

• the breadth of the rectangular plot be "x m"
• The length of the rectangular plot = (2x + 1) m

 $\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\multiput(2.1,-0.7)(0,4.2){2}{\sf \large (2x+1) m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large x m}\end{picture}$

Area of the rectangle = length × breadth

   ➔  528 m² = (2x + 1) m × (x) m

   ➔  528 = (2x + 1)(x)

   ➔  528 = 2x² + x

   ➔  2x² + x - 528 = 0

Therefore, the quadratic equation representing the given situation is

 2x² + x - 528 = 0