Q. 94.4( 33 Votes )

The area of a rec

Answer :

Given: The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one metre more then twice its breadth. 
To find: the length and the breadth of the plot.
Solution:
Let the breadth be ‘a’ m

Given, length of the plot (in metres) is one metre more then twice its breadth.

length = (2a + 1) m

Now, area of a rectangular plot is 528 m2

Area of rectangle = length × breadth

a × (2a + 1) = 528

2a2 + a – 528 = 0
In factorization, we write the middle term of the quadratic equation either as a sum of two numbers or difference of two numbers such that the equation can be factorized.

2a2 + 33a – 32a – 528 = 0

a(2a + 33) – 16(2a + 33) = 0

(2a + 33)(a – 16) = 0
⇒ (2a + 33) = 0 and (a – 16) = 0
⇒ 2a = -33 and a = 16
⇒ a = -33/2 and a = 16

As any side can never be negative,

a = 16 m
length = (2a + 1) = 2 × 16 + 1 = 33 m

Hence breadth = 16 m and length = 33 m

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Introduction to Linear Equations in Two VariablesIntroduction to Linear Equations in Two VariablesIntroduction to Linear Equations in Two Variables62 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Find the roots ofKC Sinha - Mathematics

Find the roots ofKC Sinha - Mathematics

4x2KC Sinha - Mathematics

Find the roots ofKC Sinha - Mathematics

36x2KC Sinha - Mathematics