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Ostrovityanka [42]
3 years ago
7

The shortest side of a right triangle measures 11m. The lengths of the other two sides are consecutive integers. Find the length

s of the other two sides.
Mathematics
1 answer:
uranmaximum [27]3 years ago
4 0
Interesting question.  Let the 2 unknown sides be x and x+1.
Then (11 m)^2 + x^2    = sum of the squares of the 2 shortest sides
                                     = (x+1)^2


121 + x^2 = x^2 + 2x + 1.  Then 121 = 2x + 1, and 2x = 120, or x = 60.

Then the hyp. has length 60+1= 61.

We must check these results.  Using the Pyth. Thm. (a^2 + b^2 = c^2),

11^2 + 60^2 = 61^2
121 + 3600 =  3721     This is true, so our answers are correct.

The longer side is 60 and the hyp. has length 61. 
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Answer:

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2.

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1.732= opp/ 6 in.

opp=1.732*6 in.

opp = 10.392 approximately= 10 in.

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Area of trapezium= 1/2*40*10

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2. Area of triangle= 1/2* base* height

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using Pythagorean theorem;

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17^2 = 15^2 + adj^2

289= 225 + adj^2

adj^2 = 289-225= 64

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