Name: Cross Multiplication Method: Illustration
Uploaded: 2019-07-19
Duration: 7 min 27 s
Description: This tutorial will show you many examples of solving linear equations in two variables using the cross-multiplication method with a clear step-by-step explan...

Question

The area of a rectangle decreases by $10 c m^{2}$ if the length is decreased by $5 c m$ and the breadth is increased by $3 c m$ .If the length is increased by $5 c m$ and the breadth is increased by $2 c m$ , then the area increases by $80 c m^{2}$ . Find the perimeter of the rectangle.

Accepted Answer

Let the length be $x$ and breadth be $y$

Area of rectangle $= length \times breadth$

According to the question, when the area of a rectangle gets reduced by $10 c m^{2}$ if its length is decreased by $5 c m$ and breadth is increased by $3 c m$ .

$x y - 10 = (x - 5) (y + 3)$

$\Rightarrow x y - 10 = x y + 3 x - 5 y - 15$

$\Rightarrow - 10 + 15 = 3 x - 5 y$

$\Rightarrow 3 x - 5 y = 5 . . . [i]$

Also, when length is increased by $5 c m$ and increased the breadth by $2 c m$ , the area will increase by $80 c m^{2}$ .

$(x + 5) (y + 2) = x y + 80$

$x y + 2 x + 5 y + 10 = x y + 80$

$\Rightarrow 2 x + 5 y = 80 - 10$

$\Rightarrow 2 x + 5 y = 70 . . [ii]$

Now, adding the equations $[i]$ and $[ii]$ , we get,

$3 x - 5 y + 2 x + 5 y = 5 + 70$

$\Rightarrow 5 x = 75$

$\Rightarrow x = 15 c m$

Substituting the value of $x$ in equation $[i]$ , we get,

$3 \times 15 - 5 y = 5$

$\Rightarrow 45 - 5 y = 5$

$\Rightarrow y = 8 c m$

We know that the perimeter of a rectangle $= 2 (x + y)$

$\Rightarrow 2 (15 + 8)$

$\Rightarrow 46 c m$

Hence, the perimeter of the rectangle $= 46 c m$

The area of a rectangle decreases by $10 c m^{2}$ if the length is decreased by $5 c m$ and the breadth is increased by $3 c m$ .If the length is increased by $5 c m$ and the breadth is increased by $2 c m$ , then the area increases by $80 c m^{2}$ . Find the perimeter of the rectangle.

Important Questions on Simultaneous Linear Equations

Learn and Prepare for any exam you want !

The area of a rectangle decreases by 10 cm2 if the length is decreased by 5 cm and the breadth is increased by 3 cm.If the length is increased by 5 cm and the breadth is increased by 2 cm, then the area increases by 80 cm2. Find the perimeter of the rectangle.

Important Questions on Simultaneous Linear Equations

Learn and Prepare for any exam you want !

The area of a rectangle decreases by $10 c m^{2}$ if the length is decreased by $5 c m$ and the breadth is increased by $3 c m$ .If the length is increased by $5 c m$ and the breadth is increased by $2 c m$ , then the area increases by $80 c m^{2}$ . Find the perimeter of the rectangle.