Question

a rectangular field is X to the second power - 150 x + 5400 the width in feet is x - 60 what is the length in feet​

Answer 1

Answer:

x - 90

Step-by-step explanation:

The area of a rectangle is length times width. If the width is x - 60, then the length times x - 60 equals x^2-150x+5400. Let the length be l. Then:

$(x-60)l=x^2-150x+5400$

First, we must factor the right hand side of the equation. We need two numbers that multiply to 5400 and sum to -150. Because two numbers that are negative multiplied together equals a positive number, we can just have two negative numbers that multiply to 5400 and sum to -150. Because -150 is so far from 5400, the multiples must be close to each other. We see that 60 times 90 are the closest multiples, and that 60+90 = 150.

We can factor this as (x - 60)(x-90):

$(x-60)l=(x-60)(x-90)$

Dividing both sides by (x - 60), we have:

$l = (x - 90)$