Look at the triangles shown below. What is the value of b ?

Step-by-step explanation:

In a right angled triangle, if a perpendicular is drawn from a vertex of the right angle then triangles on both sides of the perpendicular are similar.

In ΔPDY, ∠D = 90° and DM ⊥ PY

So, ΔPMD ≈ ΔDMY

If two triangles are similar then their corresponding sides are proportional.

Put

So,

According to Pythagoras theorem, square of hypotenuse is equal to sum of squares of the other two sides.

In ΔDMY,

Put

i pretty sure it is

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)