Question

The length of a rectangle is 5 mm longer than the width. If the area of the rectangle is 24 mm^2, what is the width of the rectangle?

Answer 1

Answer:

8

Step-by-step explanation:

This question is asking you to solve for the following system of equations, let x be width and y be height of the rectangle.

$\left \{ {{x=y+5} \atop {x*y=24}} \right.$

Since the former is already equal to x lets set the second equation to x

$x*y=24$

$x=24/y$

Now we have the following system of equations:

$\left \{ {{x=y+5} \atop {x=24/y}} \right.$

Now that the two equations are equal, we can solve for y:

$y+5=24/y$

Divide both sides by y

$y^2+5y=24$

Subtract 24 from the right side setting it to 0:

$y^2+5y-24=0$

Solve for y using quadratic formula:

$y=\frac{-5\pm \sqrt{5^2-4\cdot \:1\cdot \left(-24\right)}}{2\cdot \:1}$

$y=3,-8$

Given the y-values lets plug them into our original equations to find the intersections.

$x=3+5\\x=8$

Giving intersection vector (8,3)

$x=-8+5\\x=-3$

Giving intersection vector (-3,-8)

Since both the width and length of the rectangle must be positive lets use the first vector (8,3) as our solution.

The x value being 8 means the width must be 8, y value being 3 the height must be 3, these variable correlate to our original definitions of making the x value equal to the width of the carpet and y value the height of the carpet.

Answer 2

Answer:The width is 3mm

Step-by-step explanation:

Length= 5mm + width

Let the width be represented by W

Area=24mm^2

Since area= length x width

24=(5+ W) x W

24=5W +$W^{2}$

$W^{2}$ +5W-24=0

The factors are 8 and -3

$W^{2}$+8w-3w-24=0

Factorise

W(w+8)-3(w+8)=0

(w-3)=0 or (w+8)=0

W=3 0r w= -8

The width cannot be negative.

Hence,W=3mm