wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A rectangular room has a length of x m and breadth of (x+2) m and the perimeter of the room is less than 24 m. Calculate the maximum length of the room if x is a positive integer.

A
4 m
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
6 m
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
8 m
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
2 m
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 4 m
Given,
Length of the room =x m
Breadth of the room =x+2 m
Perimeter of the room < 24 m

As we know,
Perimeter of the room = 2( length + breadth)
2(x+(x+2))<24
2(2x+2))<24

Divide by 2 on both sides of the inequality,
2(2x+2))2<242
2x+2<12

Subtract 2 from both sides of the inequality,
2x+22<122
2x<10

Divide by 2 on both sides of the inequality
2x2<102
x<5

As x is a positive integer and value of x is less than 5, hence
values of x: 4, 3, 2, 1
An open circle at 5 and the red line goes to the left, indicating that x is less than 5.



Maximum value of x = 4
Hence, maximum length of the room = 4 m
Hence, option (a.) is the correct choice.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Word Problems on Algebraic Inequalities based on Mensuration
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon