Question

If the length of a rectangle is reduced by 50% and the breadth is increased is 25%, it takes the shape of a square. Find the perimeters of the rectangle and the square.

Answer 1

let length and breadth of rectangle is l and b

and side of square is a

according to question

l-l*50%=b+b*25%=a(it becomes square when length and breadth are equal)

l-l/2=b+b/4=a

l/2=5b/4=a

perimeter of rectangle is =2(l+b)

perimeter of square is = 4*a=4*l/2=2l

or. 4*a=4*5b/4=5b

Answer 2

Answer:

$\underline{ \large \mathtt{Given : }}$

• Length - 50% = 1/2
• Breadth - 25% = 1/4

$\mathtt{50\% = \frac{50}{100} = \frac{1}{2}}$

$\mathtt{25\% = \frac{25}{100} = \frac{1}{4} }$

$\underline{ \large \mathtt{to \: find: }}$

• Perimeter of Rectangle & Square
• Area of Rectangle & Square

$\underline{ \large \mathtt{formula : }}$

1. Perimeter of Rectangle - 2×(Length + Breadth)
2. Area of Rectangle - Length × Breadth
3. Perimeter of Square - 4 × Side
4. Area of Square - Side × Side

$\underline{ \large \mathtt{solution : }}$

Let the Rectangle be,

Length - x

Breadth - y

$\mathtt{Permeter \: of \: rectangle \: - 2 \times (x + y)} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \mathtt{2 \times ( \frac{1}{2} + \frac{1}{4} )} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \mathtt{\frac{2}{2} + \frac{2}{4}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \mathtt{\frac{4}{8} }\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \mathtt{\frac{1}{2} }$

$\mathtt{Perimeter \: of \: square \: - 4 \times side} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \mathtt{4 \times \frac{2}{6}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \mathtt{\frac{8}{6} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \mathtt{\frac{4}{3} }$