Apicture frame has a perimeter of 100 cm. its width is 4 cm less than twice its length. what is the width of the picture frame?

the width of the picture frame is, 32 cm

Step-by-step explanation:

Perimeter(P) of a rectangle is given by:

where,

l is the length and w is the width of the rectangle.

As per the statement:

A picture frame has a perimeter of 100 cm.

Since, the picture frame is in the form of rectangle

⇒P = 100 cm

It is given that the width is 4 cm less than twice its length

⇒

Substitute these in [1] we have;'

Combine like terms;

Divide by 2 to both sides we have;

Add 4 to both sides we have;

54 = 3l

Divide both sides by 3 we have;

18 = l

or

Substitute this in to get w;

⇒

Therefore, the width of the picture frame is, 32 cm

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0