Question

The area of rectangular remains same if its length is increased by 7 metres and breadth is decreased by 3 meters. the area remains unaffected if length is decreased by 7 metres and breadth is increased by 5 metres find dimensions of rectangle.​

Answer 1

Answer:

$\Huge{\textbf{\textsf{{\color{Magenta}{⛄A}}{\red{n}}{\purple{s}}{\pink{w}}{\blue{e}}{\green{r}}{\red{°}}{\purple{°⛄}}{\color{pink}{:}}}}}$

Step-by-step explanation:

Let’s assume the length and breadth of the rectangle be x units and y units respectively. Hence, the area of rectangle = xy sq.units From the question we have the following cases, Case 1: Length is increased by 7 metres ⇒ now, the new length is x+7 Breadth is decreased by 3 metres ⇒ now, the new breadth is y-3 And it’s given, the area of the rectangle remains same i.e. = xy. So, the equation becomes xy = (x+7)(y−3) xy = xy + 7y − 3x − 21 3x – 7y + 21 = 0 ………. (i) Case 2: Length is decreased by 7 metres ⇒ now, the new length is x-7 Breadth is increased by 5 metres ⇒ now, the new breadth is y+5 And it’s given that, the area of the rectangle still remains same i.e. = xy. So, the equation becomes xy = (x−7)(y+5) xy = xy − 7y + 5x − 35 5x – 7y – 35 = 0 ………. (ii) Solving (i) and (ii), By using cross-multiplication, we get, x = 392/14 x = 28 And, y = 210/14 y = 15 Therefore, the length of the rectangle is 28 m. and the breadth of the actual rectangle is 15 m.

Answer 2

Answer:

Let’s assume the length and breadth of the rectangle be x units and y units respectively. Hence, the area of rectangle = xy sq.units From the question we have the following cases, Case 1: Length is increased by 7 metres ⇒ now, the new length is x+7 Breadth is decreased by 3 metres ⇒ now, the new breadth is y-3 And it’s given, the area of the rectangle remains same i.e. = xy. So, the equation becomes xy = (x+7)(y−3) xy = xy + 7y − 3x − 21 3x – 7y + 21 = 0 ………. (i) Case 2: Length is decreased by 7 metres ⇒ now, the new length is x-7 Breadth is increased by 5 metres ⇒ now, the new breadth is y+5 And it’s given that, the area of the rectangle still remains same i.e. = xy. So, the equation becomes xy = (x−7)(y+5) xy = xy − 7y + 5x − 35 5x – 7y – 35 = 0 ………. (ii) Solving (i) and (ii), By using cross-multiplication, we get, x = 392/14 x = 28 And, y = 210/14 y = 15 Therefore, the length of the rectangle is 28 m. and the breadth of the actual rectangle is 15 m.

Step-by-step explanation:

hope it helps! ❣️✨