A rectangular garden has dimensions of 100 feet by 10 feet. The next season the garden decreased by two fithsof its size what is the scale drawing for the new garden show

The scale drawing for the new garden is 3:5

Step-by-step explanation:

Given;

the dimension of the rectangular garden = 100 feet by 10 feet

Size of the rectangular garden = 100 ft x 10 ft = 1000 ft²

If by next season the garden decreased by two fifth of its size, then the new size of the garden will be calculated as;

New size of the garden = old size - (²/₅ of the old size)

New size of the garden = 1000 ft² - (²/₅ x 1000 ft²)

New size of the garden = 1000 ft² - 400 ft²

New size of the garden = 600 ft²

the scale drawing for the new garden = new size / old size

= 600 ft² / 1000 ft²

= ³/₅

The scale drawing for the new garden is 3:5

That is the scale drawing of the new garden should be (√15) / 5 of the dimensions of the previous garden dimensions

Step-by-step explanation:

Here we have, dimensions of the garden = 100 ft by 10 ft

Therefore, area of the garden = 100 * 10 = 1000 ft²

The decrease in size of 2/5 its size on the next season is presented s follows;

Size decrease = 2/5 * 1000 = 400 ft²

New area of the garden = 1000 - 400 = 600 ft²

The scale drawing for the new garden is given by the relation;

Ratio of the sides of the garden = 100:10 = 10:1

Therefore, whereby the new length, l, and breadth, b, of the garden gives;

l * b = 600 ft²

l/b = 10/1

l = 10·b, which gives

10·b * b = 600

b² = 60

b = √60 = 2·√15

∴ l = 20·√15

Which gives a scale of (2·√15) / 10 = (√15) / 5

That is the scale drawing of the new garden should be (√15) / 5 of the dimensions of the previous garden dimensions.