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How to get exact surface of triangle if i only have hypotenuse and legs.

 

c=13

a+b=17 

 

I tryed to do it by the system but it is not correct and it can't get correct...

 Jun 21, 2016

Best Answer 

 #4
avatar+87 
+5

Try and use the Pythagorean Theorum. a^2+b^2=c^2

 Jun 21, 2016
 #1
avatar+36915 
0

a=12  b=5    c =13       area = 1/2 b x a  =  30 sq units

 Jun 21, 2016
 #3
avatar+118587 
0

Hi guest,

You have shown that the area will be 30 if the legs are 12 and 5 but the legs do not have to be 12 and 5.

You have not shown that the area will always be 30.

Melody  Jun 21, 2016
 #5
avatar+36915 
+5

Hey Melody..... kinda just figured that one in my head  (I do not think you can find two other values for a and b that add to 17 with a hyp of 13 ....try)        ....here is the method:

a+b =17     so b = 17-a   (1)

 

Pythagorean theorem:    a^2 + b^2 = c^2 = 13^2= 169    Substitute (1) into this

                                        a^2 + (17-a)^2 = 169

a^2 +a^2 - 34a + 289 = 169

 2 a^2 -34a + 120 = 0

a^2 -17a +60 = 0    Use Quadratic formula to get  (17+- sqrt49)/2    results in  12 and 5  

 

12-5-13 triangle    area = 1/2 a x b = 1/2   x 12  x 5 = 30 sq units

ElectricPavlov  Jun 21, 2016
 #2
avatar+118587 
+5

How to get exact surface of triangle if i only have hypotenuse and legs.

c=13

a+b=17 

I tryed to do it by the system but it is not correct and it can't get correct...

 

This is a REALLY neat question.  I do not remember seeing one like it before.

 

13 is the length of the hypotenuse.

a and b are the legs.

 

so using pythagoras's theorem we can say that

 

\(a^2+b^2=13^2\\ a^2+b^2=169 \qquad (1)\\~\\ \mbox{We also know that }\\ a+b=17\\ \mbox{Squaring both sides we get}\\ a^2+b^2+2ab=289\qquad (2)\\~\\ \mbox{Solve equation 1 and 2 simultaneously}\\ (2)-(1)\\ 2ab=289-169\\ 2ab=120\\ ab=60\\ \frac{1}{2}ab=30\\ \mbox{This is the formula for the area of the triangle so the area is }30units^2 \)

 Jun 21, 2016
 #4
avatar+87 
+5
Best Answer

Try and use the Pythagorean Theorum. a^2+b^2=c^2

JakefromStateFarm Jun 21, 2016

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