Answer
Verified
425.4k+ views
Hint : Create equations on the basis of given conditions.
Let the length of the rectangle be $x$ metres and the breadth be $y$ metres.
Area of the rectangle $ = length \times breadth = x \times y = xy$ sq. metres
From the given information, we have,
\[(x + 3) \times (y - 4) = xy - 67\]
& \[(x - 1) \times (y + 4) = xy + 89 \\\]
$
(x + 3) \times (y - 4) = xy - 67 \\
= > xy - 4x + 3y - 12 = xy - 67 \\
= > 4x - 3y = 55 \\
= > 4x = 3y + 55....(i) \\
$
Also,
$
(x - 1) \times (y + 4) = xy + 89 \\
= > xy + 4x - y - 4 = xy + 89 \\
= > 4x - y = 93....(ii) \\
$
Substituting equation (i) in equation (ii), we get,
$
4x - y = 93 \\
= > 3y + 55 - y = 93 \\
= > 2y = 38 \\
= > y = 19 \\
$
Substituting $y = 19$ in equation (i), we get,
$
4x = 3y + 55 \\
= > 4x = 3(19) + 55 \\
= > 4x = 112 \\
= > x = 28 \\
$
Therefore, the length of the rectangle $ = x = 28$ metres.
breadth of rectangle $ = y = 19$ metres.
Note – In this problem, first let assume the breadth and length of the rectangle then follow the given conditions which gives us two equations. On solving these two equations, we get the final answer.
Let the length of the rectangle be $x$ metres and the breadth be $y$ metres.
Area of the rectangle $ = length \times breadth = x \times y = xy$ sq. metres
From the given information, we have,
\[(x + 3) \times (y - 4) = xy - 67\]
& \[(x - 1) \times (y + 4) = xy + 89 \\\]
$
(x + 3) \times (y - 4) = xy - 67 \\
= > xy - 4x + 3y - 12 = xy - 67 \\
= > 4x - 3y = 55 \\
= > 4x = 3y + 55....(i) \\
$
Also,
$
(x - 1) \times (y + 4) = xy + 89 \\
= > xy + 4x - y - 4 = xy + 89 \\
= > 4x - y = 93....(ii) \\
$
Substituting equation (i) in equation (ii), we get,
$
4x - y = 93 \\
= > 3y + 55 - y = 93 \\
= > 2y = 38 \\
= > y = 19 \\
$
Substituting $y = 19$ in equation (i), we get,
$
4x = 3y + 55 \\
= > 4x = 3(19) + 55 \\
= > 4x = 112 \\
= > x = 28 \\
$
Therefore, the length of the rectangle $ = x = 28$ metres.
breadth of rectangle $ = y = 19$ metres.
Note – In this problem, first let assume the breadth and length of the rectangle then follow the given conditions which gives us two equations. On solving these two equations, we get the final answer.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
State the differences between manure and fertilize class 8 biology CBSE
Why are xylem and phloem called complex tissues aBoth class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
What would happen if plasma membrane ruptures or breaks class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What precautions do you take while observing the nucleus class 11 biology CBSE
What would happen to the life of a cell if there was class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE