Question

pls help me my exam tomorrow just doubt in this question ​

Answer 1

Perimeter of Rectangle=2(Length+Breadth)

Given, Perimeter=240 cm

Let Length=x

Breadth=y

Then

2(x+y)=240

x+y=240/2

x+y=120 cm

x=120-y cm

X=120-y (Equation 1)

Now

Length is Decreased by 10%

$= x - (x \times 10\%) \\ \\ = x - (x \times \frac{10}{100} ) \\ \\ = x - \frac{x}{10} \\ \\ = \frac{9x}{10}$

Now

Length=9x/10 cm

Breadth Increase by 20%

$= y + (y \times 20\%) \\ \\ = y + (y \times \frac{20}{100} ) \\ \\ y + \frac{y}{5} \\ \\ = \frac{6y}{5}$

We get Breadth =6y/5 cm

Perimeter=240 cm

A/Q

2(l+b)=240

$2( \frac{9x}{10} + \frac{6y}{5} ) = 240 \\ \\ 2( \frac{9 (120 - y)}{10} + \frac{6y}{5} ) = 240 \\ \\ 2( \frac{1080}{10} - \frac{9y}{10} + \frac{6y}{5} ) = 240 \\ \\ 2( \frac{1080}{10} \frac{ - 18y + 12y}{10}) = 240 \\ \\ 2( \frac{1080}{10} - \frac{6y}{10} ) = 240 \\ \\ = \frac{2160}{10} - \frac{12y}{10} = 240 \\ \\ - \frac{12y}{10} = 240 - \frac{2160}{10} \\ \\ - \frac{12y}{10} = \frac{2400 - 2160}{10} \\ \\ \cancel - \frac{12y}{10} = \cancel - \frac{240}{10} \\ \\ y = \frac{240}{10} \times \frac{10}{12} \\ \\ y = 20$

We go y=20

We know

x=120-y

x=120-20

x=100

Length=100 cm

Breadth=20 cm

$\boxed{\mathbf{\huge{Length=100\:cm}}}$

$\boxed{\mathbf{\huge{Breadth=20\:cm}}}$