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

Question

Find the length x. Express your answer in simplified radical form.

right triangle left side 51ft, bottom 45ft, right side x

picture a triangle one side 51 ft, one side 45ft and last side x

Answer 1

where is the right angle in the triangle. Between the right and bottom, between the bottom and left? Without knowing this, we can't tell you the answer.

BUT
in a right triangle
hypotenuse squared = side 1 squared + side 2 squared

Answer 2

I'm assuming that the legs have the lengths 51 and 45.

For this use the pythagorean theorm, a^2 + b^2 = c^2, with a and b being legs, and c being the hypotenuese of the triangle (the longest side).

51^2 + 45^2 = x^2
2601 + 2025 = x^2
4626 = x^2
sqrt(4626) = x
sqrt(9*514) = x --- you can factor the number inside the square root and then take the square root of just that part
3sqrt(514) = x

Answer 3

if you are saying the legs are 51 and 45, then

a^2 + b^2 = c^2
51^2 + 45^2 = c^2
c^2 = 2601 + 2025
c^2 = 4626
c = sqrt(4626)
c = sqrt(2 * 9 * 257)
c = 3sqrt(514)

ANS : 3sqrt(514)

The reason it can be heard to understand is because of the right triangle is turned left or right, the left and right side will change. I am assuming that the right side is the hypothenuse.

If not, then using 45^2 + b^2 = 51^2, b = 24

Answer 4

If the right side is the hypotenuse (the side of a right triangle opposite the right angle), then in simplified radical form (leaving the square root):

x = sqrt( 51^2 + 45^2)
= sqrt(2601 + 2025)
= sqrt(4626)

Hope this helps!

Answer 5

I am assuming the hypotenuse is x.

51^2 +45^2=c^2
2601+2025=x^2
4626=x^2
3times the square root of 514=x

If it is not, and the 51 is, it's a lot easier

x^2 +45^2=51^2
x^2 +2025=2601
x^2=576
x=24

Answer 6

pythagorean theorom: a^2 + b^2 = c^2
where a and b are the shorter sides and c is the longest side (known as the hypotanuse). So plug 51 and 41 in and solve.

Answer 7

if x is the hypotnuse(the longest side) the it's 51^2+45^2=x^2 so x = 68.014704

Answer 8

4 < x <20 If you are looking for an exact answer, something is missing from the problem. Is this a right triangle? Were one of the angles given?

Answer 9

Sounds like Pythagorean Theorem problem, but can't tell from your description which side is the hypotenuse.