Question

One leg of a right triangle is 6 inches longer than the other leg. The hypotenuse of the triangle is 25 inches.

What is the length of each leg to the nearest inch? Separate answers using commas.

Answer 1

@shamil98

Answer 2

do you know the pythagorean theorem? Asquared + Bsquared=C squared, C being the hypotenuse.

Answer 3

\[x ^{2} + (x+6)^{2} = 25^{2}\]

Answer 4

Pythagorean Theorem,

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

Where a and b are the legs, and c is the hypotenuse.

\(\therefore x^2+(x+6)^2=25^2\)

Answer 5

When you do the math for the left side, you have to FOIL out that sum of x+6.

\((x+6)^2=(x+6)(x+6)=x^2+12x+36\)

So inputting,

\(x^2+x^2+12x+36=625\)

Combine like terms,

\(2x^2+12x+36=625\)

Then you can move the 625 over so that you have a nice quadratic equation.

\(2x^2+12x-589=0\)

Now, you can use the quadratic equation,

\(\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a},~\text{when}~ax^2+bx-c=0\)

Answer 6

so then what would the lengths be?

Answer 7

You should be able to do that yourself! It is spelled out for you above :)

Answer 8

sorry, I didnt see it, my computer wasn't showing it, but I refreshed the page and now it's all good! thanks!

Answer 9

No problemo!

Answer 10

so when I put it in the quadratic formula, this is the work I did:

\[2x^2 + 12x - 589 = 0\]
\[x = \frac{-(12)^2 \pm \sqrt{(12)^2 - 4(2)(-589)}}{ 2(2) }\]
\[x = \frac{-144 \pm \sqrt{144 - 4,712} }{ 4 }\]

then what would I do from there @austinL

Answer 11

You made an error, it is -b not -b^2

Answer 12

where at?

Answer 13

\(\displaystyle x=\frac{\color{red}{-b}\pm\sqrt{b^2-4ac}}{2a},~\text{when}~ax^2+bx-c=0\)

Answer 14

oh oh okay! so then it's \[x = \frac{ -12 \pm \sqrt{144 - 4,712} }{ 4 }\]

Answer 15

\(\displaystyle x = \frac{ -12 \pm \sqrt{144 - (-4,712)} }{ 4 }\)

Answer 16

\[x = \frac{ -12 \pm \sqrt{4,856} }{ 4 }\]

Answer 17

Correctomundo.

You will get two answers, one is impossible because it would make a leg longer than the hypotenuse.

So as a result you should get,
\(x=\sqrt{\dfrac{607}{2}}-3\approx 14.421\)
Then the other leg is x+6

Answer 18

okay, so how would i find the last leg?

Answer 19

\(x=\sqrt{\dfrac{607}{2}}-3\)
\(x+6=(\sqrt{\dfrac{607}{2}}-3)+6=\sqrt{\dfrac{607}{2}}+3\)

Answer 20

well you have x and x + 6 would just be 14.421 + 6.

Answer 21

so all the legs are 25, 14.421, and 20.421?

Answer 22

all inches of course.

Answer 23

No, legs are the decimals. Hypotenuse is 25.

Answer 24

oh right, okay! you guys helped so much!

Answer 25

My pleasure! and good job!

Answer 26

thank you:)