Question

5. A rectangular playground 75 m x 45 m has a jogging track of width 3.7 m along its inside edges.Find the area of the jogging track.
6. A rectangular mat of 5 m x 3.5 m had a border of width 1.8 m all around it. If the cost of the mat
is 272/m², find the cost for bordering the mat.​

Answer 1

Q. 5

Given data : A rectangular playground 75 m x 45 m has a jogging track of width 3.7 m along its inside edges.

To find : Find the area of the jogging track ?

Solution : Let, length of playground be 75 m and breadth of be 45 m.

Here, we know that due to jogging track one rectangle is developed inner side of jogging track.

⟹ length of rectangle inside jogging track = Length of rectangular playground - 2{width of jogging track}

⟹ length of rectangle inside jogging track = 75 - 2{3.7}

⟹ length of rectangle inside jogging track = 75 - 7.4

⟹ length of rectangle inside jogging track = 67.6 m

similarly,

⟹ breadth of rectangle inside jogging track = breadth of rectangular playground - 2{width of jogging track}

⟹ breadth of rectangle inside jogging track = 45 - 2{3.7}

⟹ breadth of rectangle inside jogging track = 45 - 7.4

⟹ breadth of rectangle inside jogging track = 37.6 m

Now,

⟹ area of rectangular playground = length * breadth

⟹ area of rectangular playground = 75 * 45

⟹ area of rectangular playground = 3375 m²

similarly,

⟹ area rectangle inside jogging track = length * breadth

⟹ area rectangle inside jogging track = 67.6 * 37.6

⟹ area rectangle inside jogging track = 2541.76 m²

Now,

⟹ Area of jogging track = area of rectangular playground - area rectangle inside jogging track

⟹ Area of jogging track = 3375 - 2541.76

⟹ Area of jogging track = 833.24 m²

Answer : Area of the jogging track is 833.24 m²

Q. 6

Given data : A rectangular mat of 5 m x 3.5 m had a border of width 1.8 m all around it. If the bordering cost of the mat is Rs 272/m².

To find : find the cost for bordering the mat ?

Solution : Let length of mat be 5 m and breadth of mat be 3.5 m.

Here, we know that due to border of rectangular mat one rectangle is developed outer side of border of rectangular mat.

Now,

⟹ length of rectangle outer side of boder =

length of mat + 2{width of border}

⟹ length of rectangle outer side of boder =

5 + 2{1.8}

⟹ length of rectangle outer side of boder = 5 + 3.6

⟹ length of rectangle outer side of boder = 8.6 m

similarly,

⟹ breadth of rectangle outer side of boder =

breadth of mat + 2{width of border}

⟹ breadth of rectangle outer side of boder =

3.5 + 2{3.6}

⟹ breadth of rectangle outer side of boder = 3.5 + 3.6

⟹ breadth of rectangle outer side of boder = 7.1 m

Now,

⟹ area of rectangular mat = length * breadth

⟹ area of rectangular mat = 5 * 3.5

⟹ area of rectangular mat = 17.5 m²

similarly,

⟹ area of rectangle outer side of boder = length * breadth

⟹ area of rectangle outer side of boder = 8.6 * 7.1

⟹ area of rectangle outer side of boder = 61.06 m²

Now,

⟹ area of boder of rectangular mat = area of rectangle outer side of boder - area of rectangular mat

⟹ area of boder of rectangular mat = 61.06 - 17.5

⟹ area of boder of rectangular mat = 43.56 m²

Here, we know the bordering cost of the mat is Rs 272/m².

So now,

⟹ bordering cost of the mat = 43.56 * 272

⟹ bordering cost of the mat = Rs 11848.32

Answer : Bordering cost of the rectangular mat is Rs 11848.32