Question

HELP FAILING GEOMETRY!!!!

What are the values of a and b?

a. A = 9/2 , B= 15/2
b. A = 15/2 , B = 9/2
c. A = 16/3 , B = 15/2
d. A = 9/2 , B = 13/2

Answer 1

@jigglypuff314
@chrisboen26

Answer 2

Isnt this simple division?

Answer 3

pythagorean theorem is a^2 + b^2 = c^2
" a " and " b " being the legs of the right triangle
and " c " being the hypotenuse

so looking at the picture you can get that
b^2 = 6^2 + a^2
and (8+a)^2 = 10^2 + b^2
isolate b^2 in the second to get -> b^2 = (a+8)^2 - 10^2
and since b^2 = b^2

solve for " a " for
6^2 + a^2 = (a+8)^2 - 10^2

Answer 4

Ugh I get what you are saying but I honestly don't know how to do that equation

Answer 5

don't know how to solve for " a " from
6^2 + a^2 = (a+8)^2 - 10^2 ?

Answer 6

It's alright if you don't :)

6^2 + a^2 = (a+8)^2 - 10^2 simplify

36 + a^2 = (a+8)(a+8) - 100 FOIL

36 + a^2 = a^2 + 16a + 64 - 100 simplify and subtract a^2 from both sides
-a^2 -a^2

to get 36 = 16a - 36 then add 36 to both sides
+36 +36

so 16a = 72 then divide both sides by 16
/16 /16

so a = 72/16 simplified =

Answer 7

Omgosh Thank you soo much and I am getting help with Geometry from my teacher just kinda need help with it.


And simplified it would be 9/2 ! So that eliminates b and c and leaves a and d

Answer 8

yep :)

then you can plug what you got for " a "
into
b = √(a^2 + 36)
so b = √((9/2)^2 + 36)
then b = √(81/4 + 36)

Answer 9

There is a theorem that helps with this problem.

Right Triangle Altitude Theorem Part a: The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse.

Right Triangle Altitude Theorem Part b: If the altitude is drawn to the hypotenuse of a right triangle, each leg of the right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg.

Answer 10

So B would equal to 15/2? The way I did it made the number into a decimal but I change it into a fraction

Answer 11

Thank you @mathstudent55 That helps a lot. So the answer would be A? @jigglypuff314

Answer 12

b = 15/2 is what I got :)

Answer 13

Thank you so much @jigglypuff314

Answer 14

Using Part a of the theorem, 6 is the geometric mean of 8 and a.

That means: \(\dfrac{8}{6} = \dfrac{6}{a} \)

Solve for a.

Answer 15

I got a as 24 but that makes no sense. It has to be a fraction and the way jiggly puff said it makes sense.

Answer 16

8a = 36
a = 36/8 = 9/2

Now you can use part b of the theorem to find b.

Answer 17

OHHHH I TOTALLY GET IT NOW . Thank you both for your amazing help this makes perfect sense now