Question

The perimeter of a rectangle is 20cm and its area is 24 cm^2. calculate the length and width of the rectangle.

using quadractic equation.



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Answer 1

see explanation

Explanation:

let length be l and width be w , then perimeter P is

P = 2(l + w)

given P = 20 , then

2(l + w) = 20 ( divide both sides by 2 )

l + w = 10 ( subtract w from both sides )

l = 10 - w → (1)

area (A) is calculated as

A = lw

given A = 24 , then

lw = 24

substitute l = 10 - w into this equation

(10 - w)w = 24

10w - w² = 24 ( subtract 24 from both sides )

10w - w² - 24 = 0 ( multiply through by - 1 and rearrange )

w² - 10w + 24 = 0 ← in standard form

(w - 4)(w - 6) = 0 ← in factored form

equate each factor to zero and solve for w

w - 4 = 0 ⇒ w = 4

w - 6 = 0 ⇒ w = 6

substitute these values into (1)

w = 4 : l = 10 - 4 = 6

w = 6 : l = 10 - 6 = 4

Then

length = 6 cm , width = 4 cm

or

length = 4 cm , width = 6 cm