Question

please help!! medal and fan
Find the value of X.

4
Sq.root 23
6
Sq.root 63
https://rialto5819-ehs-pps.gradpoint.com/Resource/2146263,72F,0,0,0,0,0/Assets/testitemimages/geometry_a/similarity/mc074-1.jpg

Answer 1

a.4
b. \[2 \sqrt{3}\]
c.6
d. \[6\sqrt{3}\]

Answer 2

Incomplete question?what is x?

Answer 3

then what is y?

Answer 4

it dont say for x nor y and it just wants y

Answer 5

If we call the height of this triangle (the segment perpendicular to the base) 'h', then using the pythagorean theorem we get the following equations:\[\bf h^2+3^2=x^2\]\[\bf h^2+9^2=y^2\]We also know that the large right triangle has a hypotenuse 9 + 3 = 12 so applying the pythagorean theorem once again we get the equation:\[\bf x^2+y^2=12^2\]Substituting the equations for x^2 and y^2 we get:\[\bf (h^2+3^2)+(h^2+9^2)=12^2\]Let's now simplify and solve for 'h':\[\bf 2h^2+90=144 \implies 2h^2=54 \implies \pm h^2=27 \implies h=\sqrt{27}\]Since 'h' is the height, it can't be a negative value so we discard the negative solution. Hence our only solution is: \[\bf h=\sqrt{27}\]Now that we know the height 'h', we can use it to find the 'x' and 'y' by plugging it in to the first 2 equations we came up with:\[\bf (\sqrt{27})^2+3^2=x^2 \implies 36 = x^2 \implies x = 6\]\[\bf (\sqrt{27})^2+9^2=y^2 \implies 108=y^2 \implies y = \sqrt{108}=6\sqrt{3}\]And we are done.

@knowel

Answer 6

thank you

Answer 7

what if your trying to find x do that formula works

Answer 8

@genius12

Answer 9

@knowel Yes. It allows you to find both x and y in this case.

Answer 10

ok and when you simplyedfiy how did you get 54

Answer 11

nm thank you