Math, asked by aryaman8324, 8 months ago

The perimeter of a right angled triangle is 60cm, it's hypotenuse is 26cm find its area​

Answers

Answered by mjecintha
0
Which class I mean like which std
Answered by michellemeel12
1

Answer:

Step-by-step explanation:

Let’s call each side a, b, and c respectively, where c is the hypotenuse.

If  a+b+c=60  and  a2+b2=c2  and we know that  c=26 , then we have enough information to work this out.

The area can be written as  ab2 , which is the same as base * height over 2.

Therefore, using the above equations,

a+b+26=60  

a+b=34  

Also,

a2+b2=676  

One way to solve this problem is to square the first equation,

(a+b)2=342  

a2+b2+2ab=1156  

Oh, cool! We can substitute the  a2+b2  in the above equation with our second equation!

a2+b2=676  

676+2ab=1156  

Subtract 676 from both sides, we get:

2ab=480  

Since the area of said right triangle can be expressed as  ab/2 , all we have to do now is divide by 4 both sides of the equation!

ab2=120  

The area of this triangle is  120cm2 . If you’re wondering what the sides are, they are 2 4  and  10 .

One way to get this is to check the factors of 26:

1,2,13  and  26 .

The only Pythagorean triple with relatively prime integers that include one of these numbers is the set  (5,12,13) .

So multiplying every side by 2, we get the set  (10,24,26) .

There’s another way… using the equations  a+b=34  and  ab=240 . If you’re interested in this solution, read on:

a=34−b  

b(34−b)=240  

Expanding, we get  34b−b2=240 . With the formula

x=−b±b2−4ac√2a  

Where  ax2+x+c=0 , we can express this as  −b2+34b−240=0 .

a=−1  

b=34  

c=−240  

x=−34±342−960√−2  

x=−34±196√−2  

x=−34±14−2  

x1=10,x2=24  

Now thanks to this handy formula, we now have the possible values of  b !

(a,b)=(10,24)  or  (24,10)  

Since it’s a triangle it doesn’t really matter. The side lengths are 10, 24 and 26.

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