What is the value of x in the diagram?

5

Step-by-step explanation:

Pythagoras : a^2 + b^2 ≈ c^2

so, x^2 + (2x+2)^2 = (2x+3)^2

=> x^2 + 4x^2 + 8x + 4 = 4x^2 + 12x + 9

=> x^2 = 4x + 5

=> x^2 - 4x - 5 = 0

now solve the quadratic equating. a little bit of creative thinking and trying with the options of a (x-a)×(x+b)=0 approach (multiplying and adding of factors need to give us -5 but only -4x in the result, so we try a=-5 but then b=1 as "correcting" factor), and yes

(x-5)×(x+1) = x^2 - 4x - 5 = 0

this is only true, if at least one of the multiplication factors are 0.

so, x-5=0 or x+1=0. or both, but that is not possible.

x-5=0, when x=5.

x+1=0, when x=-1

-1 as the length of a side does not make any sense.

so, the only valid solution is x=5

answer: given that the roller coaster can accommodate 1600 riders per hour, thus the roller coaster can accomodate 1600 / 60 = 26.67 riders per minute.

given that there are 345 people in the line, the number of minutes it will take for the 345 persons to get into the roller coaster is given by 345 / 26.67 = 12.94 minutes.

therefore, it will take you 12.94 minutes to get to the front of the line.

step-by-step explanation: