Question

perimeter of square equal to Rectangular box is 100 cm . If length of Rectangular box is 1/4th of Breadth. then calculate area of Rectangular box. ​

Answer 1

Solution

Given :-

• Perimeter of square = 100 cm
• perimeter of square is equal to Rectangular box.
• If length of Rectangular box is 1/4th of Breadth.

Find :-

• Area of rectangular box.

Explanation

Let,

• Length be Rectangular box = x cm
• Breadth be Rectangular box = y cm

Using Formula

★ perimeter of Square = (side)×4

★ perimeter of rectangular box = 2(Length + Breadth)

So,

According to question

==> perimeter of Square = perimeter of rectangular box

==> 100 = 2(x + y)

==> x + y = 100/2

==> x + y = 50_____________(1)

Again,

==> x = 1/4 × y

==> 4x = y

==> 4x - y = 0_________(2)

Sum equ(1) & equ(2)

==> x + 4y = 50

==> 5x = 50

==> x = 50/5

==> x = 10.

keep in equ(1)

==> 10 + y = 50

==> y = 50 - 10

==> y = 40

Hence

• Length of rectangular box be = 10 cm
• Breadth of rectangular box. be = 40 cm.

________________________

Now, Calculate area of rectangular box.

Using Formula

★ Area of rectangular box = Length × Breadth

==> Area of rectangular box = 10 × 40

==> Area of rectangular box = 400 cm²

___________________________

Answer 2

$perimeter \: of \: the \: square \: is \: given \: by \: = {side}^{2}$

Area of the rectangle = length × breadth

$l \times b = 100cm \: (given)$

$also \: given \: that \: l = \frac{b}{4}$

Therefore , substituting the value l = b/4 in area of rectangle, we get :

$\frac{ {b}^{2} }{4} = 100$

${b}^{2} = 400$

$b = 20cm$

Therefore,

$l = \frac{20}{4} = 5cm$

$therefore \: area \: of \: the \: rectangle \: is \: \\ l \times b \: = 5 \times 20 = 100 {cm}^{2}$