Math, asked by Hatdogcheese, 5 months ago

The length of a wooden frame is 1 foot longer than its width and its area is equal to 12ft.^2

Answers

Answered by anmolvashisht80
2

Answer:

length = 4ft

width = 3ft

Step-by-step explanation:

These are the given:

A = lw

l = x + 1ft

w = x

A = 12ft

We'd equate the product of the values of length (l) and width (w) to 12, following the formula of an area. Solution below.

12 = (x+1)(x) substitute and distribute (multiply) x to x + 1

12 = x² + x this should be the result. then transfer the product to the left side of the equal sign.

12 - x² - x = 0 this should be the result. remember that when you transfer a term to the other side of the equal sign, you change the term's sign to its opposite. arrange the terms now.

-x² - x + 12 = 0 this should be the result. the quadratic term (-x²) shall not be negative. thus, we multiply all the terms to -1 to make the quadratic term positive.

x² + x - 12 = 0 this should be the result. factor them.

(x+4) (x-3) = 0 this should be the result. equate each of them to zero now.

x + 4 = 0

x = -4

but since a measurement can't be negative, this value of x is not applicable.

x - 3 = 0

x = 3

we're gonna use this one.

Checking:

12 = lw

12 = (x+1) (x)

12 = (3+1) (3)

12 = (4) (3)

12 = 12

therefore, the value of x is right.

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