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May 20th, 2019, 07:00 PM   #1
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Algebra word problem

The formula for the length of the hypotenuse of a right-angled triangle, whose short sides are p, q is r² = p² + q²


1. Make p the subject of this formula.


2. Evaluate the shortest side of a right-angled triangle, if the other two sides have lengths given by q = 9.3 and r = 11.4. State the answer accurate to 1 d.p.

Last edited by skipjack; May 21st, 2019 at 07:26 AM.
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May 20th, 2019, 07:47 PM   #2
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Math Focus: Algebraic Geometry
$\displaystyle r^{2} = p^{2}+q^{2}$

$\displaystyle r^{2} - q^{2} = p^{2}$

$\displaystyle \sqrt{r^{2} - q^{2}} = p$

You should be able to go from here, if not, let me know.
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Last edited by Greens; May 20th, 2019 at 07:47 PM. Reason: Latex
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May 20th, 2019, 08:38 PM   #3
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So does p = √(r+q)(r-q), -√(r+q)(r-q)?

Last edited by skipjack; May 21st, 2019 at 07:32 AM.
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May 20th, 2019, 10:39 PM   #4
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Quote:
Originally Posted by helpmeddddd View Post
-√(r+q)(r-q)?
Since we're dealing with triangle lengths, we can't have negative length.
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May 21st, 2019, 07:35 AM   #5
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p = √(r² - q²) suffices.

If q = 9.3 and r = 11.4, what value does that give you for p (to 1 d.p.)?
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May 21st, 2019, 11:42 AM   #6
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p≈6.59 so p= about 6.6


is there a good formula to use for this?
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Last edited by helpmeddddd; May 21st, 2019 at 11:53 AM.
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May 21st, 2019, 01:47 PM   #7
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https://en.m.wikipedia.org/wiki/Pythagorean_theorem

So in your case: $p^{2}+q^{2} = r^{2}$
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May 21st, 2019, 03:23 PM   #8
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Quote:
Originally Posted by helpmeddddd View Post
State the answer accurate to 1 d.p.
That requirement is unclear. It doesn't tell you to round your answer or to truncate your answer. What exactly does "accurate to 1 d.p." mean?
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May 21st, 2019, 03:29 PM   #9
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Quote:
Originally Posted by helpmeddddd View Post
The formula for the length of the hypotenuse of a right-angled triangle, whose short sides are p, q is r² = p² + q²
1. Make p the subject of this formula.
2. Evaluate the shortest side of a right-angled triangle, if the other two sides have lengths given by q = 9.3 and r = 11.4.
Are you a student attending math classes?

If so, seems to be something wrong with your teacher...
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May 21st, 2019, 07:43 PM   #10
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Quote:
Originally Posted by Greens View Post
https://en.m.wikipedia.org/wiki/Pythagorean_theorem

So in your case: $p^{2}+q^{2} = r^{2}$
why am I finding the length of r as I already know it?
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