Area of Rectangular Paths

Q.

A square and a rectangle have equal areas. If each side of the square is $18cm$ and the width of the rectangle is $12cm,$ find the length of the rectangle.

Q. A rectangular park measuring 12 m by 8 m is to be bordered by external path which is 2 m wide. Find the area of the path.

1. $192m^2$
2. $144m^2$
3. $92m^2$
4. $96m^2$

Q.

The length of a rectangular field is $10m$ and breadth is $4m$. If a square field has the same perimeter as this rectangular field, find which field has the greater area.

Q. Length and breadth of rectangle ABCD are $l$ cm and $b$ cm respectively. If width of green coloured path is $w$ cm, then which of the following represents brown coloured area

1. $(l+b-w)w$
2. $lb-(l+b-w)w$
3. $lb+(l+b-w)w$
4. $lb-(l+b+w)w$

Q.

The perimeter of a rectangle of sides $24$ cm and $16$ cm is equal to the perimeter of a square. Find the side and area of the square.

Q. A path $2m$ long and $1m$ broad is constructed around a rectangular ground of dimensions 120 $m$ and $90m$ respectively. Find the area of the path.

Q.

A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area $ ?$

(a) (b)

Q. In the given figure area of square BCFG is 64 $c{m}^2$ and is 4 times the area of ABGH .If the area of rectangle ABGH is equal to that of CDEF then find perimeter of ADEH.

1. 20 cm
2. 40 cm
3. 16 cm
4. 10 cm

Q.

A square has side length of $16.5\mathrm{in}$

If the area is multiplied by $9$, what happens to the side length?

1. The side length is doubled.

2. The side length is multiplied by 4.5

3. The side length is multiplied by 9

4. The side length is tripled.

Q.

The perimeter of the square whose area is $16m{m}^2$ is.

1. $16mm$

2. $16m$

3. $4mm$

4. $4m$

Q. A triangle ABC stands on a rectangle BCDE and AF is a perpendicular from A to DE. If $AB=6.5m,CD=5m,AF=7.5m$, then BC can't be less than

1. 6 m
2. 5.1 m
3. 7.04 m
4. 6.5 m