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.
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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
___________________________
Answered by
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Area of the rectangle = length × breadth
Therefore , substituting the value l = b/4 in area of rectangle, we get :
Therefore,
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