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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

Grade 7 - Mathematics
Area of Rectangular Path - III

Example:
A path of uniform width runs around and outside a square plot of side 20 metres. If the area of the path is 276 square metres find its width.

Solution:
Let the width of the path be x metres.
Now each side of the given square plot = 20 metres.
Therefore, each side of the outer square = (20 + 2x) metres, because the path runs outside.
The are of the path = (The area of outer square) - (The area of the inner square)
= (20 + 2x)2 - 202
But the area of the path is given to be 276 square metres.
Therefore, (20 + 2x)2 - 202 = 276
(20 + 2x)2 = 202 + 276
(20 + 2x)2 = 400 + 276
(20 + 2x)2 = 676
Take square roots on both sides
(20 + 2x)2 = 676
20 + 2x = 26
2x = 26 - 20
2x = 6
x = 6/3
\ The width of the path = 3 metres.


Directions: Read the above example carefully and answer the following questions:

  • Draw a square plot of side 12 centi-metres and label its sides. Draw a path of uniform width around and outside the square plot. If the area of the path is given by 256 square centi-metres, then find the width of the path. Use different colors to represent the path and the square plot.


Q 1: A path of uniform width runs around and outside a square plot of side 25 metres. If the area of the path is 399 square metres find its width.
3 metres
3.5 metres
2 metres
2.5 metres

Q 2: A path of uniform width 4 metres runs around and outside a square plot. If the area of the path is 288 square metres find a side of the square plot.
14 metres
45 metres
5 metres
15 metres

Q 3: A path of uniform width runs around and outside a square plot of side 15 metres. If the area of the path is 400 square metres find its width.
5 metres
3 metres
4 metres
2 metres

Q 4: A path of uniform width runs around and outside a square plot of side 18 metres. If the area of the path is 517 square metres find its width.
5.5 metres
4 metres
4.5 metres
5 metres

Question 5: This question is available to subscribers only!

Question 6: This question is available to subscribers only!


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