Find the length of the hypotenuse?

Question

In a right-angeled triangle, one side is 7 cm and another is halfaslong as the hypotenuse. Find the length of the hypotenuse

Answer 1

about 8.1

Answer 2

First we would label the shorter leg X. and when you consider that the longer leg is 2cm more effective tahn the shorter leg, we would lable the longer leg X+2. because the hypotenuse is 2cm longer than the longer leg, its length will be equivalent to (X+2)+2 or in reality X+4. then you ought to apply the pythagorean thereom (a squared+bsquared = c squared, the position c is the hypotenuse) to create an equation. So let a=X, let b =X+2, c=X+4 (x)^2+(X+2)^2=(X+4)^2 that's your equation, and one you component out the exponents you get: X^2+X^2+4X+4=X^2+8X+16 now integrate like words: 2X^2+4X+4=X^2+8X+16 next, you want to make the equation equivalent to 0, so that you subtract whats on the right of the equivalent signal. X^2-4X-12=0 you are able to now use the quadratic formula (x=-b+-Sq. root(b^2-4ac)/2a) to locate the fee of x, (a is a million, b is -4, c is -12) AFter fixing with the formula you need to get x to be both 6 or -2 becuase of the plus or minus signal. when you consider that we are coping with triangles, the length of X must be efficient, eliminating -2 as an answer. So X=6. X+2=6+2=8. X+4=6+4=10. you need to get 6 for the shorter area, 8 for the longer area, and 10 for the hypotenuse. i wish that permits!

Answer 3

Let us call the length of the hypotenuse h . Then the length of the other unknown side will be ½h

Thus, h² = 7² + (½h)² = 49 + ¼h²
Therefore, h² - ¼h² = 49
¾h² = 49
h² = 49 x 4 ÷ 3 = 196 ÷ 3
h = square root of (196 ÷ 3)
= 8·0829 (approx. 8·08cm)

Answer 4

let the length of hypotenuse = x
one side = 7 cm.
second side = x/2
we have x^2 = 7^2 + (x/2)^2
x^2 - x^2/4 = 49
3x^2/4 = 49
x^2 = 49*4/3
x = square root of (49 * 4/3)
= 7 * 2 /sq.root 3
x = 8.08 cm. Ans.

Answer 5

Guess the second leg is x. Then the hypotenuse = 2x.
Now Pythagoras: 7^2 + x^2 = (2x)^2
Or: 49 = 3x^2. So x^2 = 49/3 and x = 7/root(3)
(The negative possibility you can forget here).
The hypotenuse = 2 * 7/root(3) = 8.08...

Th

Answer 6

You know this is a 30-60-90 triangle because one leg is half the hypotenuse. In these triangles, you divide the longer leg by sqrt(3) to get the shorter leg. The shorter leg in this case is 7/sqrt(3) = 7sqrt(3)/3, so the hypotenuse is 14sqrt(3)/3.

Answer 7

H= SQ Root of 65.31

H Squared= (7 squared) + (H/2 Squared)
Solve for H
H= Square Root of 49 times 4/3

Answer 8

Let's call the hypoteneus 'h'.
By the pythagorean Theorem:
7^2 + (1/2 h)^2 = h^2.
With a little algebra, we have:
49 + 1/4 h^2 = h^2,
49 = 3/4 h^2,
196/3 = h^2,
h = 14/(square_root(3)).

I hope this is clear enough.

Answer 9

Use the equation a^2 + b^2 = c^2 where c is the hypotenuse.

7^2 +(0.5c)^2 = c^2

49 + 0.25c^2 = c^2

49 = 0.75c^2

65.33 = c^2

c=8.08 cm

Answer 10

You apply Pitagorean equation:

x² + y² = h²

x=7 cm
y = 0.5 h
h = ?

2) Substitute the given values:

7² + 0.5h² = h²

Solve for h:
7² =h²-0.5h²
0.5h² = 7²
h² = 7²/0.5
h² = 98 cm²
h = 9.89 cm (just take the positive value of the square root)

That's it!

Good luck!

Answer 11

Hey...all you have to do is translate this to an equation. Use a^2+b^2=c^2. a = 7, b=.5h, and c=h. Solve for h.