find the length of the hypotenuse?

Question

The hypotenuse of a right triangle is 2cm. more than the longer leg,while the longer leg is itself 2cm more than the shorter leg.Find the length of the hypotenuse.
can someone help and explain to me how to do it?

Answer 1

Let the shorter leg have length x.

The longer leg has length x + 2.

The hypotenuse has length x + 4.

Use the Pythagorean Theorem:

x^2 + (x + 2)^2 = (x + 4)^2

x^2 + x^2 + 4x + 4 = x^2 + 8x + 16

2x^2 + 4x + 4 = x^2 + 8x + 16

x^2 - 4x - 12 = 0

(x - 6)(x + 2) = 0

x = 6 or x = -2

A length cannot be negative, so the shorter leg has length 6 cm.

The longer leg has length 8 cm.

The hypotenuse has length 10 cm.

(This is a common Pythagorean triple, by the way, so you could have found the answer like that. :D )

Answer 2

First we would label the shorter leg X. And since the longer leg is 2cm larger tahn the shorter leg, we would lable the longer leg X+2. Since the hypotenuse is 2cm longer than the longer leg, its length would be equal to (X+2)+2 or basically X+4. Then you must use the pythagorean thereom (a squared+bsquared = c squared, where 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 is your equation, and one you factor out the exponents you get:
X^2+X^2+4X+4=X^2+8X+16
now combine like terms:
2X^2+4X+4=X^2+8X+16
next, you want to make the equation equal to zero, so you subtract whats on the right of the equal sign.
X^2-4X-12=0
now you can use the quadratic formula (x=-b+-Sq. root(b^2-4ac)/2a) to find the value of x, (a is 1, b is -4, c is -12)
AFter solving with the formula you should get x to be either 6 or -2 becuase of the plus or minus sign. Since we are dealing with triangles, the length of X must be positive, eliminating -2 as an answer. So X=6. X+2=6+2=8. X+4=6+4=10. You should get 6 for the shorter side, 8 for the longer side, and 10 for the hypotenuse. I hope that helps!

Answer 3

Lets call the shortest leg x. Then the longer leg is x+2, and the hypotenuse is x+4.
So x^2 + (x+2)^2 = (x+4)^2, using pythagoras.
Expanding each side:
x^2 + x^2 + 4x + 4 = x^2 + 8x + 16
x^2 - 4x - 12 = 0
(x-6)(x+2) = 0
x = 6 or x =-2
Obviously we can't have side length -2, so x = 6.
So its a 6-8-10 triangle, so the hypotenuse is 10cm.

Answer 4

enable us call the size of the hypotenuse h . Then the size of the different unknown area will be ½h subsequently, h² = 7² + (½h)² = 40 9 + ¼h² hence, h² - ¼h² = 40 9 ¾h² = 40 9 h² = 40 9 x 4 ÷ 3 = 196 ÷ 3 h = sq. root of (196 ÷ 3) = 8·0829 (approx. 8·08cm)

Answer 5

let the shorter of the two legs be x cm
longer leg=x+2cm
length of the hypotenuse
=longer leg +2
=x+2+2
=x+4
now applying the Pythagoras theorem
a^2+b^2=c^2
x^2+(x+2)^2=(x+4)^2
x^2+x^2+4x+4=x^2+8x+16
adding -x^2-8x-16
x^2-4x-12=0
(x-6)(x+2)=0
x=6
so thepythagoran triplets are
6,8,10 cm
the length ofthe hypotenuse=10cm

Answer 6

Start out with what you know. c = b +2, b = a + 2, and
c² = a² + b² Substitute
(a+4)² = a² + (a + 2)² so that
a² + 8a + 16 = 2a² + 4a +4 and
a² -4a - 12 = 0
Now solve the quadratic and use the positive root for the length of the smallest leg (a), and calculate b and c from that.


Doug

Answer 7

let x=shorter leg
then x+2=longer leg
then x+4=hypotenuse

x^2+(x+2)^2=(X+4)^2

x^2 +x^2 +4x +4=x^2 +8x +16

simplfy..
X^2-4x-12=0

solve for x
(x-6)(x+2)=0
x=6,-2
since distance can't be negative, x=6
so, 6+4=10 is the hypotenuse

Answer 8

short is A long is A+2 hypo is A+4 formula is a squared plus b squared equals c squared so its A squared plus (A+2)squared equals (A+4) squared. solve agebraically for A

Answer 9

assume hypotneuse as (x+2)cm, long side as xcm n short side as (x-2)cm
use pythogoreon theorem,
(x+2)(x+2)=(x)(x) X (x-2)(x-2) n solve
then x=0 or 8
therefore hypotneuse=10 since x is unequal to zero.