The perimeter and the area of a rectangular sheet are 42 m and 108 m2, respectively. The length of the diagonal is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 15 m.
Area of rectangle = L × B = 108
Perimeter of rectangle = 2(L + B) = 42
L + B = 21 m
⇒B = 21-L
So,
Area = 108
(L) × (21-L) = 108
⇒ 21L - L² = 108
Solving the equation we get
L = 12, 9
So
If Length = 12 m and breadth = 21 - 12 = 9
If Length = 9 m and breadth = 21 - 9 = 12
Now
Diagonal = √(length2 + breadth2)
⇒ √(122 + 92) = √(144 + 81)
⇒ √225
⇒ 15