Question

A park is in the shape of a right angled triangle. fencing of grass beds is to spread along the longest side of the park. if one side of the park is 60 m and it’s area is 1350 m², then find the cost of spreading the grass bed at the rate of Rs.20 per metre length.

Answer 1

Rs 1500

Explanation:

Given:

• One side of the park is 60 m (base).
• The area of the park is 1350 m².
• The rate of spreading grass bed is Rs.20 per meter length

To find:

• Length of the longest side of the park
• Cost of spreading the grass bed

Solution:

Let the length of the longest side of the park be h.

The area of the park can be calculated using the following formula:

`\boxed{\bold{Area = (1)/(2) * base * height}}`

Substituting value:

1350 =
`(1)/(2)*60*h`

Doing criss cross multipication:

h=1350*
`(2)/(60)`

h = 45 m

Since we find the two sides of the right-angled triangle.

The longest side is its hypotenuse:

let base= b, height be c, and hypotenuse or longest side be c.

By using Pythagoras' theorem:

`\bold{c^2=a^2+b^2}`

Substituting value:

`c^2=45^2+60^2`

`c=√(5625)`

c=75 m

Therefore, the length of the longest side of the park is 75 m.

Now again,

we have:

the cost of spreading the grass bed = rate* length of longest side

=20*75

=Rs1500

Therefore, the cost of spreading the grass bed is Rs 1500.

#Nepal