Question

show your solutions follow the steps and then answer ​

Answer 1

Step-by-step explanation:

Step -1:-

Given that

A rectangular garden has an area of 84m² and a perimeter of 38 m.

Find its length and width.

Step-2:-

We know that

Area of a rectangle = length × width sq.units

=> length × width = 84 m²

=> l×w = 84

=> lw = 84 ------------(1)

And

Perimeter of a rectangle = 2(l+w)

=> 2(l+w) = 38

=> l+w = 38/2

=> l+w = 19 ------------(2)

=> l = 19-w -------------(3)

Step-3:-

Using (3) , on substituting it in (1) then

=> (19-w)(w) = 84

=> 19w - w² = 84

=> 19w-w²-84 = 0

=> -w² + 19w - 84 = 0

On multiplying with -1 both sides

=> w² - 19w + 84 = 0

=> w²-7w-12w +84 = 0

Step-4:-

w²-7w-12w +84 = 0

=> w(w-7)-12(w-7) = 0

=> (w-7)(w-12) = 0

=> w-7 = 0 (or) w-12 = 0

=> w = 7 (or) w = 12

So, width = 7 m or 12 m

If the width is 7 m then length

= 19-7 = 12 m

If the width is 12 m then length

= 19-12 = 7 m

Answer :-

The length and the breadth of the rectangular garden are 12 m and 7 m (or)

7 m and 12 m respectively.

Used formulae:-

→ Area of a rectangle = length × width sq.units

→ Perimeter of a rectangle = 2(l+w)