Question

A rectangle has an area (x2-17x+72) square units.Since the area of a rectangle is determined using the formula, A= lw, what could be the length and width of the rectangle

Answer 1

geez this is a doozy

okay first factor the binomial using binomial theorem. you probably don't remember that (at least I didn't) so here it is.


`{x}^(2) - 17x + 72`
you have to figure out what two numbers add to -17 and multiply together to make 72

so make a table of all the numbers that add to 17 then multiply them together and see of they make 72. since it's -17 we will need to use two negative numbers:

-1 * -16 = 16
-2 * -15 = 30
-3 * -14 = 42? idk
-4 * -13 = something, math is hard
keep going until...
-8 * -9 = 72

so it's -8 and -9 are the factors we want.
we wrote this as:


`(x - 8)(x - 9)`
seeing this equal as our area in the a=l*w formula gives:


`(x - 8)(x - 9) = l * w`
Now, plug in a number greater than 9.
It has to be greater than 9 because anything less than that would give us a negative area. Let's use 10 because it's easy. It doesn't matter which number you use as long as it's greater than 10. The problem appears to say it just wants a possible length and width, not a specific answer.


`(10 - 8)(10 - 9) = lw`

`2 = lw`
so factors of 2.
length could be 1 and width could be 2 or vice versa.

you could also choose a different number than 10. let's try 20.


`(14 - 8)(14 - 9) = lw`

`(6)(5) = lw`

`30 = lw`
so lw could also be 10 and 3 in this case. or 5 and 6. or 1 and 30. all these answers would be correct.

Answer 2

length: 9

width: 8

Explanation:

you would need to factorise the equation in order to work out the length and width of the rectangle

so to factorise x^2 -17x +72, you will need to numbers that multiply to make 72 and add to make -17

the numbers are -9 and -8

so the factorised equation is (x-9)(x-8)

if you equate it to 0 you get 9 and 8 as values for x

since the length is longer than the width

the length is 9 and the width is 8