Find The Difference Between Length and Breadth? If

A man takes 6 km distance to go around the rectangular area. If the area of the rectangle is 2 km, find the difference between length and breadth.

1. 2 km
2. 0.75 km
3. 1 km
4. 0.5 km
Anurag Mishra Professor Asked on 14th August 2015 in

Explanation:-
Let the length of the rectangle area is L km & the breadth of the rectangle area is B km.

A man takes 6 km distance to go around the rectangular area.
Then, the perimeter of the rectangle area = 6 km

Formula-
Perimeter of the rectangle area = 2 (L + B)

Then, 2(L + B) = 6
L + B  = 6/2
L + B = 3 km

The area of the rectangle area = 2km

Formula-
The area of the rectangle area = L x B

Then, L B = 2
Formula-
(a + b)2 = a2 + b2 + 2 a b
Then, (L + B)2 = L2 + B2 + 2 L B
Now, put the value of L + B = 3  & L B = 2
Then, (3)2 = L2 + B2 + 2 x 2
9 = L2 + B2 + 4
L2 + B2 = 9 – 4
L2 + B2 = 5

Formula-
(a – b )2 = a2 + b2 – 2 a b
Then, (L – B)2 = L2 + B2 – 2 L B
Now, put the value of L2 + B2 = 5 & L B = 2
Then, (L – B)2 = 5 – 2 x 2
(L – B)2 = 1
L – B = 1
Then, difference between length & breadth is 1 km
Hence, the answer is (3) 1 km.

Anurag Mishra Professor Answered on 14th August 2015.