Find length x in each triangle. Express your answer in simplified radical form.?

To answer that question you need to know the Pythagorean Theory which states

a ^ 2 (squared) + b ^ 2 = c ^ 2

c= the hypotenuse

so a= 8 b= x and c= 12

8^2 + x^2 = 12 ^ 2

64 + x^2 = 144

x^2 = 80 (144-64)

x= (squareroot of 80) 8.9442719

And round it off however you need.

it would be 4 radical 5.

see: 12 *12=144 and 8 *8=64.

subtract. 144 -64=80

simplify. find the highest perfect square that 80 can divide into. it's 16 *5 . so now you have the square root of 16 *5. simplify out the 16 to get a 4 outside of the radical and you're left with a 5 inside.

apply the Pythagorean theorem on this problem:

given:

h=12, b (bottom or base)= 8

required:

a( altitude)

solution:

using the formula of Pythagorean theorem which is:

c^2 = a^2+b^2

a^2= c^2-b^2

substitute the values:

a^2= 12^2 - 8^2

therefore: a= square root of 80 ; or a=8.94

ok. i don't know what you precisely mean via backside and middle and section, yet I presume the the proper option attitude exists between the backside and the middle, and the section is the hypotenuse. if so, x^2 = 15^2 + 20^2 = 225 + 4 hundred = 625, subsequently x = 25. besides the shown fact that if x is doubtless one in all the hands of the the proper option attitude, then, the hypotenuse is of length 20. subsequently, x^2 = 20^2 - 15^2 = 4 hundred - 225 = one hundred seventy five subsequently x = 13.23.

12^2 = 8^2 + x^2

144 = 64 + x^2

80 = x^2

(16*5) = x^2

4*sqrt(5) = x

12squared equals 8squared plus x squared.

144 = 64 + x^2

x^2 = 80

x = square root 80

x = 4 sqrt 5

oooh...trigonometry/geometry?

Pythagorean theorem:

a squared (side) + b squared (side) = c squared (hypotenuse)

this only works with right triangles (ones with 90 degree angles)

so...8 squared + b squared = 12 squared

64 + b squared = 144

subtract 64

b squared = 80

square root of 80 = 4 root 5

b (or in your case, x) = 4 root 5

hope this helped

12x12=144

8x8 = 64 -

..........

x 80

x is sqr root of 80 = 8.944