Question

And artificial lake is in the shape of a rectangle and has an area of 9/20 square mi.² the width of the lake is 1/5 the length of the lake what are the dimensions of the lake

Answer 1

The dimensions of lake are length 1.5 miles and width 0.3 miles

Solution:

Given that,

Artificial lake is in the shape of a rectangle

Let the length of lake be "a"

The width of the lake is 1/5 the length of the lake

`width = (length)/(5)\\\\width = (a)/(5)`

The area of lake is 9/20 square miles

The area of rectangle is given by formula:

`Area = length * width`

Substituting the values we get,

`(9)/(20) = a * (a)/(5)\\\\a^2 = (9)/(20) * 5\\\\a^2 = (9)/(4)\\\\\text{Taking square root on both sides }\\\\a = (3)/(2) = 1.5`

Thus, we get

`length = a = 1.5 \text{ miles }\\\\width = (a)/(5) = (1.5)/(5) = 0.3 \text{ miles }`

Thus the dimensions of lake are length 1.5 miles and width 0.3 miles