Question

A right triangle has an area of 138 unit sq and perimeter of 60.94 units. Find the length of hypotenuse.

Answer 1

@terenzreignz :P

Answer 2

Always one for the weird problems...
Let's try doing it algebraically... we need two values, the lengths of the legs of said right triangle... Let's call them x an dy

Answer 3

x and y

Answer 4

Now, the area of a right triangle is just half the product of the measures of the legs... so...
\[\Large \frac12xy = 138\]

Answer 5

And the perimeter of the right triangle is just the sum of the measures of the sides... so...
\[\Large x+y+h=60.94\]
where h is the length of the hypotenuse...

Answer 6

yup,i wrote these 2 equations already ,now what :P

Answer 7

Now, you solve the system? What else? :P

Answer 8

lol

Answer 9

x=60.94-y-h
(60.94-y-h)(y)=138*2 o.O

Answer 10

...
\[\Large h = 60.94-x-y\]\[\Large \sqrt{x^2+y^2}=60.94-x-y\]

Answer 11

yes,what after this?

Answer 12

I don't know, square both sides?
\[\Large x^2 + y^2 = (60.94-x-y)^2\]

Answer 13

a-b-c omg

Answer 14

huh?

Answer 15

(a-b-c)^2
gotta be huge..hmm

Answer 16

You're not exactly known for posting easy questions :P

Answer 17

\[\Large x^2 + y ^2 = 60.94^2 -121.88(x+y)+(x+y)^2\]

Answer 18

will we get answer from this? :P

Answer 19

Let's see. Expand...
\[\Large x^2 + y ^2 = 60.94^2 -121.88(x+y)+x^2+2xy + y^2\]\[\Large \cancel{x^2} + \cancel{y ^2} = 60.94^2 -121.88(x+y)+\cancel{x^2}+2xy + \cancel{y^2}\]

Answer 20

\[\Large 0 = 60.94^2 -121.88(x+y) + 2xy\]

Answer 21

and we know 2ab's value

Answer 22

i mean 2xy

Answer 23

Let's use this...
\[\Large \frac12xy = 138\]
Multiply both sides by 4, we get...
\[\Large 2xy = 552\]

Answer 24

yup

Answer 25

\[\Large 0 = 60.94^2 -121.88(x+y)+552\]

Answer 26

x+y is nearly 35

Answer 27

(x+y)^2=x^2+y^2+2xy
x^2+y^2=552

Answer 28

Well, we could replace \(\Large y \) with \[\Large \frac{276}x\]

Answer 29

wait what

Answer 30

sqrt(552)=23.49 o.O

Answer 31

??

Answer 32

How?

Answer 33

I got (x+y) from ur equation i.e 35
now expand
\[\Huge (x+y)^2=x^2+y^2+2xy\]
now isolate x^2+y^2 and take the sqrt

Answer 34

I see.
Well, good, I suppose, did you really need help with this? :P

Answer 35

I'm not good at spotting the quick ways to solve problems... better fix that :D

Answer 36

we are getting sqrt{552} it should be sqrt{673}
hmm..

Answer 37

okay i got it :P

Answer 38

Great... LOL

Answer 39

So... why did you drag me into it? :P

Answer 40

to spend some time :D

Answer 41

Well, time well-spent, I suppose :P

Answer 42

haha