9. A rectangle's length is 5 cm less than twice
its width. If the length is decreased by 5 cm
and width is increased by 2 cm; the perimeter
of the resulting rectangle will be 74 cm. Find
the length and the width of the original
rectangle.
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Answers
Answer :
›»› The length of a rectangle is 25 cm and the breadth of a rectangle is 15 cm.
Given :
- A rectangle's length is 5 cm less than twice its width. If the length is decreased by 5 cm and width is increased by 2 cm.
- The perimeter of the resulting rectangle will be 74 cm.
To Find :
- The length of a rectangle and the width of a rectangle.
Solution :
Let us assume that, width of a rectangle is x cm.
As it is given that, a rectangle's length is 5 cm less than twice its width.
→ 2x - 5.
As it is also given that, the length is decreased by 5 cm
→ 2x - 5 - 5
→ 2x - 10 cm.
As it is also given that, the width is increased by 2 cm.
→ x + 2 cm.
As we know that
→ Perimeter of rectangle = 2(length + width)
→ 74 = 2{(2x - 10) + (2x + 2)}
→ 74 = {(2 * 2x) - (2 * 10) + (2 * x) + (2 * 2)}
→ 74 = {4x - (2 * 10) + (2 * 2x) + (2 * 2)}
→ 74 = {4x - 20 + (2 * x) + (2 * 2)}
→ 74 = {4x - 20 + 2x + (2 * 2)}
→ 74 = {4x - 20 + 2x + 4}
→ 74 = 4x + 2x - 20 + 4
→ 74 = 6x - 20 + 4
→ 74 = 6x - 16
→ 74 + 16 = 6x
→ 90 = 6x
→ 90 = 6x
→ x = 90/6
→ x = 15
Therefore,
→ Width of a rectangle = x
→ Width of a rectangle = 15 cm.
→ Length of a rectangle = 2x - 5
→ Length of a rectangle = 2 * 15 - 5
→ Length of a rectangle = 30 - 5
→ Length of a rectangle = 25 cm.
Hence, the length of a rectangle is 25 cm and the breadth of a rectangle is 15 cm.
Answer:
length = 25 cm and breadth = 15 cm
Step-by-step explanation:
Let length of rectangle be 'x' and breadth be 'y'.
According to the question:-
x = 2y - 5
x - 2y = -5 ---------> equation-1
We know perimeter of rectangle is :-
Perimeter = 2(length + breadth) = 74
From the question:-
length becomes 'x- 5' and breadth becomes 'y+2'.
So, 2(x -5 + y + 2) = 74
2(x +y -3) = 74
2x + 2y -6 = 74
2x +2y = 80
Now divide entire equation by 2
x + y = 40 --------> equation-2
Subtract equation-2 from equation-1
x - 2y = -5
x + y = 40
- - -
=> -3y = -45
3y = 45
y = 45/3 = 15
Putting value of y in equation-1
x -2×15 = -5
x -30 = -5
x = -5 + 30
x = 25
Hope it helps you!