Question

The perimeter of a rectangular metal plate is 36 dm and its area is 80
dm^2. Find its dimensions. (Relate the measures to the sum and product of a
quadratic equation.)​

Answer 1

Answer:

length = 8 or 10 dm

width = 8 or 10 dm

Step-by-step explanation:

perimeter = 2X (l+b)

36= 2 X (l+b)

36/2 = l+b

18= l+b

l=18-b

Area = l X b

80= (18-b) X b

80= 18b - b^2

b^2 - 18b +80 =0

by solving quadratic equation

b^2 -18b+80

b^2 -(10+8)b + 80

b^2 -10b -8b +80

b(b-10) -8(b-10)

(b-10) (b-8)

b=10 or b= 8

and

l= 18-b

putting the value of b in this equation we get

l= 8 or 10

.

.

relating the sum and product of a quadratic equation

α= 10, β= 8

a = 1, b= -18 , c = 80

sum of zeros = α+ β = -b/a

10+8= -(-18)/1

18=18

product of zeros = αβ= c/ a

80= 80/1

80=80