About Soroban Expertise I have a systematic and orderly way to organize the facts in a word problem, which (usually) leads clearly to the necessary equation. I think I can help with all types of word problems.
Experience 38 years of teaching college-level math, mostly at a two-year college.
Education/Credentials BS and MS in mathematics, SUNY Albany
Expert: Soroban Date: 3/9/2008 Subject: word problem
Question QUESTION: The hypotenuse of a right triangle has a length of 13 cm. The sum of the lengths of the two legs is 17 cm. Find the lengths of the legs.
ANSWER: Hello, Anan!
Let a = length of one leg
Let b = length of other leg
We are told that: a + b = 17 --> b = 17 - b [1]
The hypotenuse is 13.
From Pythagorus: a² + b² = 13² [2]
Substitute [1] into [2]: a² + (17 - b)² = 169
This simplifies to: 2a² - 34a + 120 = 0
Divide by 2: a² - 17a + 60 = 0
which factors: (a - 5)(a - 12) = 0
and has roots: a = 5, 12
Substitute into [1] and get: b = 12, 5
The lengths of the legs are 5 and 12 cm.
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---------- FOLLOW-UP ----------
QUESTION: Hi! I was just wondering how the a^2 + (17-b)^2 = 169 became (2a)^2 - 34a + 120 = 0 ?
Thanks
Answer Hello, Anan!
>> How did a^2 + (17-b)^2 = 169 become (2a)^2 - 34a + 120 = 0 ?
