Question

Find the lengths of altitudes of the triangle whose sides are given by 3x-4y=5,4x+3y=5and x+y=1

Answer 1

Length of altitude on x + y = 1  is √2 /10

Step-by-step explanation:

3x-4y=5,4x+3y=5and x+y=1

Altitude on x+y=1

3x-4y=5

4x+3y=5

Solving x = 35/25 = 7/5

y = -1/5

Vertex =(7/5 , - 1/5)

Slope of x + y = 1

is - 1

Slope of altitude = -1/-1 = 1

y = x + c

=> -1/5 = 7/5 + c

=> c = -8/5

=> y = x - 8/5

=> 5y = 5x - 8

=> 5x - 5y  = 8

   x + y = 1

=>10x = 13

=> x= 13/10

   y = -3/10

(13/10 , - 3/10)

Distance between =(7/5 , - 1/5)  & (13/10 , - 3/10)

= √(7/5 - 13/10)² + (-1/5 + 3/10)²

= √1/100 + 1/100

= √2 /10

Length of altitude on x + y = 1  is √2 /10

Similarly we can find others altitude

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