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beks73 [17]
3 years ago
12

Find the value of y.​

Mathematics
1 answer:
Bess [88]3 years ago
8 0

Answer:

=6√3 the third option.

Step-by-step explanation:

We can use the Pythagoras theorem to find the value of y. We need two equations that include y.

a²+b²=c²

c=9+3=12

x²+y²=12²

x²=144 - y².........i (This is the first equation)

We can also express it in another way but let us find the perpendicular dropped to c.

perpendicular²= x²-3²=x²-9 according to the Pythagoras theorem.

y²=(x²-9)+9²

y²=x²+72

x²=y²-72....ii( this is the second equation

Let us equate the two.

y²-72=144-y²

2y²=144+72

2y²=216

y²=108

y=√108

In Surd form √108=√(36×3)=6√3

y=6√3

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\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\&#10;\begin{array}{ccccccccc}&#10;&&x_1&&y_1&&x_2&&y_2\\&#10;%  (a,b)&#10;&B&(~{{ -3}} &,&{{6}}~) &#10;%  (c,d)&#10;&C&(~{{ 4}} &,&{{ 0}}~)&#10;\end{array}&#10;\\\\&#10;-------------------------------\\\\&#10;BC=\sqrt{[4-(-3)]^2+[0-6]^2}\implies BC=\sqrt{(4+3)^2+(0-6)^2}&#10;\\\\\\&#10;BC=\sqrt{7^2+(-6)^2}\implies \boxed{BC=\sqrt{85}}\\\\&#10;-------------------------------

\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\&#10;\begin{array}{ccccccccc}&#10;&&x_1&&y_1&&x_2&&y_2\\&#10;%  (a,b)&#10;&C&(~{{ 4}} &,&{{0}}~) &#10;%  (c,d)&#10;&D&(~{{ 2}} &,&{{ -1}}~)&#10;\end{array}&#10;\\\\&#10;-------------------------------\\\\&#10;CD=\sqrt{(2-4)^2+(-1-0)^2}\implies CD=\sqrt{(-2)^2+(-1)^2}&#10;\\\\\\&#10;\boxed{CD=\sqrt{5}}\\\\&#10;-------------------------------

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