find the length of each leg.?

Question

The hypotenuse of a right triangle is 13ft. the longer leg is two more then twice the length of the shorter side. find the length of each leg.

Answer 1

13^2 = x^2 + (2x +2)^2

169 = x^2 + 4x^2 + 8x + 4

169 = 5x^2 + 8x + 4

5x^2 + 8x + -165 = 0

(5x + 33)(x - 5) = 0

5x + 33 = 0 x = - 33/5
and
x - 5 = 0 x = 5

It doesn't make sense for the length to be negitive so x = 5

the other is 2x + 2 = 2(5) + 2 = 12

Answer 2

L = Longer leg length
S = Shorter leg length

L^2 + S^2 = 13^2 from the Pythagorean theorem
L = 2 + 2S from the problem statement

Substitute for L in the first equation
(2 + 2S)^2 + S^2 = 169

Expanding
4 + 8S + 4S^2 + S^2 = 169

Combining and rearranging
5S^2 + 8S - 165 = 0

Use the quadratic formula to solve for S
Use L = 2 + 2S to solve for L

Or...
simply remember that 5-12-13 is a right triangle, just like 3-4-5 always is

Answer 3

Using a^2 + b^2 = c^2
(2x + 2)^2 + x^2 = 13^2
(2x + 2)(2x + 2) + x^2 = 169
4x^2 + 8x + 4 + x^2 = 169
5x^2 + 8x + 4 -169= 0
5x^2 + 8x -165 = 0
(apply quadratic equation)
-8 +/- sqrt(8^2 - 4(5)(-169)) / 2(5)
-8 +/- sqrt(64 + 3300) / 10
-8 +/- sqrt(3364) / 10
-8 +/- 58 /10
(using negative) x = -66/10
x = -6.6 since a length cannot be neagtive.....
(using poistive) X = +50/10
x = 5
(proof)
a^2 + b^2 = c^2
(2x + 2)^2 + x^2 = 13^2
x= 5
(2(5) + 2)^2 + 5^2 = 169
12^2 + 25 = 169
144 + 25 = 169
169 = 169

Answer 4

because of the fact this is an isoceles suited triangle, the legs are equivalent, and consequently Pythagorea's theorem a^2 + b^2 = c^2 would surely be a^2 + a^2 = 2a^2 = c^2. all of us recognize c = 80 one, consequently 2 a^2 = 80 one ^2 2 a^2 = 6561 a^2 = 6561 / 2 = 3280.5 a = sqrt (3280.5) = fifty seven.27 each and every leg would degree approx fifty seven.27

Answer 5

i know one combination that fits the profile. use the pythagorean triple 5 - 12 - 13. therefore the two legs are 5 ft and 12 ft. respectively.

Answer 6

(13)² = x² + (2x + 2)²

(2x + 2)(2x + 2) = 4x² + 4x + 4x + 4 = 4x² + 8x + 4

- - - - - - - - - -

169 = x² + 4x² + 8x + 4

169 = 5x² + 8x + 4

169 - 169 = 5x² + 8x + 4 - 169

0 = 5x² + 8x - 165

(5x + 33)(x - 5)

- - - - - - - - - - - - - - s-

Answer 7

Uggh I hate math. Good luke.