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13 votes
13 votes
The hypotenuse of right triangle is 226 miles long. The difference between the other two sides is 194 miles. Find the missing sides. Use exact values.

Find the value of the short and ling leg.

User Mark Sherretta
by
3.0k points

1 Answer

22 votes
22 votes

Answer: short line: 30 miles, ling leg: 224 miles

Explanation:

Intro:
We will be using Pythagoras theorm, which states, if we have a 90 degree triangle which has 3 side as H, B and P defined as Hypotenuse, Base and Perpendicular, then H² = B² + P²
In your case, we know that hypotenuse is 226.

We also know that (A + B)² = A² + B² + 2AB

Given:
H = 226

B - P = 194


Solution:
B = 194 + P
So
(226)² = (194 + P)² + P²

51076 = (194)² + P² + (2 x 194 x P) + P²

51076 = 37636 + 2P² + 388P

51076 - 37636 = 2P² + 388P
13440 = 2P² + 388P

6720 = P² + 194P

P² + 194P - 6720 = 0
P² - 30P + 224P - 6720 = 0
P(P - 30) + 224(P - 30) = 0
(P - 30) x (P + 224) = 0
P = 30 or -224
As miles cannot be negative, we will choose answer as 30 miles.

Now we have H = 226 and P = 30
Using Pythagoras theorm:
(226)² = (30)² + B²
51076 = 900 + B²
50176 = B²

B = 224 miles.

So the missing miles are 224 miles and 30 miles

User Neha Chopra
by
3.0k points
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