Question

Answer this 1
There is a rectangular onion storehouse in the farm of Mr. Ratnakar at Delhi. The length of rectangular base is more than its breadth by 7 metre and the diagonal is more than length by 1 metre. find the length and breadth of this storehouse.

Answer 1

There is a rectangular onion storehouse in the farm of Mr. Ratnakar at Delhi. The length of rectangular base is more than its breadth by 7 metre and the diagonal is more than length by 1 metre. Find the length and breadth of this storehouse.

Step by step explanation :

Let the breadth of the storehouse be 'x' metres.

Thus, As per your question,

Length = (x + 7) m

Diagonal = (x + 7 + 1) m = (x + 8) m

Thus, We can solve this question by Pythagoras theorem,

$\tt{x{}^{2} + (x + 7){}^{2} = (x + 8){}}^{2}$

$\tt \small{x{}^{2} + x{}^{2} + 14x + 49 = x{}^{2} + 16x + 64}$

Cancelling x^2 on both sides,

$\tt \small{x{}^{2} + 14x - 16x + 49 - 64 = 0}$

$\tt{x{}^{2} -2x - 15 = 0}$

Thus, Now solving this equation by factorization method.

$\tt{x{}^{2}- 5x +3x -15 = 0}$

$\tt{x(x - 5)+3(x - 5)= 0}$

$\tt{(x+3) =0\:or\:(x-5) =0}$

$\tt{x=-3 \:or\:x = 5}$

But,

We know that,

Length is never negative.

$\tt{\therefore x≠ - 3}$

So, x = 5.

Breadth of storehouse = 5m.

Length = x + 7 = 5 + 7 = 12m.

Thus,

Length of the base of storehouse is 12 m whereas breadth is 5 m.

Answer 2

$\underline{\mathfrak{\huge{Question:}}}$

There is a rectangular onion storehouse in the farm of Mr. Ratnakar in Delhi. The length of rectangular base is more than its breadth by 7 metres and the diagonal is more than length by 1 metre. find the length and breadth of this storehouse.

$\underline{\mathfrak{\huge{Answer:}}}$

For this question, we can form some terms :-

Let the Breadth of the Rectangle be = x

Length of the rectangle = x + 7

Diagonal of the rectangle = x + 7 + 1 = x + 8

=》 Now, due to the Pythagoras Theorem:-

$H^{2} = B^{2} + P^{2}$

Put the values in the formula :

=》 $(x + 7)^{2} + x^{2} = (x + 8)^{2}$

=》 $x^{2} + 49 + 14x + x^{2} = x^{2} + 64 + 16x$

=》 $x^{2} - 2x - 15 = 0$

=》 $x^{2} - 5x + 3x - 15 = 0$

=》 $x ( x - 5 ) + 3 ( x - 5 ) = 0$

=》 ( x + 3 ) ( x - 5 ) = 0

=》 ( x + 3 ) = 0 ; ( x - 5 ) = 0

=》 x = (-3) ; 5

Since the breadth can't be negative, it will be 5 m

Breadth = 5 m

Length = x + 7 = 5 + 7 = 12 m

There's your answer !