Question

Mario is looking for the dimensions of the rectangular garden that has an area of 14m² and a perimeter of 18 meters. Write in quadratic equation standard form

Answer 1

Answer:

Step-by-step explanation:

Let x and y be length and breadth of garden respectively

xy=14m^2-----(1)

x=14/y---(2)

2(x+y)=18 meters---(3)

Substituting 2 in 3:

2(14/y+y)=18

28/y  + 2y=18

Multiplying everything by y:

28+2y^2=18y

2y^2-18y+28---->This is the quadratic equation in standard form

or y^2-9y+14=0

y^2-2y-7y+14=0

y(y-2)-7(y-2)=0

(y-2)(y-7)=0

y=2 or 7 and x=7 or 2 respectively

If want different method, look at pic

PLEASE MARK BRAINIEST

Answer 2

Answer:

The required quadratic equation is b² - 9b +14 = 0, where 'b' is the breadth of the rectangle

Step-by-step explanation:

Given,

Area of the rectangular garden = 14m²

Perimeter of the rectangular garden = 18m

To find,

The quadratic equation using these values

Recall the concept

Area of a rectangle = l×b

Perimeter of a rectangle = 2(l+b)

Where 'l' is the length and 'b' is the breadth of the garden.

Solution:

Let

Since perimeter of the rectangular garden is 18m, we have

2(l+b) = 18

l+b = 9

l = 9 - b ---------------(1)

Since the area of the rectangular garden is 14m², we have

lb = 14

Substituting the value of 'l' from equation (1) we get

(9-b)b = 14

9b - b²  = 14

9b - b²- 14 = 0

b² - 9b +14 = 0

Hence the required quadratic equation is b² - 9b +14 = 0, where 'b' is the breadth of the rectangle

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