How many arrangements are there using the word INUKSHUK that begin with letter u

Answer;If we measure the shadow of the monument and the shadow of one of the persons, at the same moment, we can use the first Thales' Theorem to calculate the height of the inushuk, knowing the height of the person.  

It should be noted that to apply Thales' Theorem, it is necessary to establish the two triangles are similar, that is, that they have the corresponding angles equal or that their sides are proportional to each other.  

Having this established, the theorem is:  

Two triangles are similar when they have equal angles and proportional sides  

In this case of the inukshuk and the person, we have two similar triangles (Figure attached) where  is the height of the inukshuk,  is the height of the person,  is the length of the shadow of the inukshuk and  is the length of the shadow of the person.  

In addition, because both triangles are similar, their angles are similar as well. This means that the relation between two sides of the big triangle is equal to the relation between two sides of the small triangle:  

All these lengths can be directly measured, except H, which is the value we want to to find.  

So, in order to approach this problem we have to find H from equation (1):  

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240