SOLUTION: one leg of the right traingle is 5 iches longer than the other leg. if the hypotenuse measures 25 inches, find the length of each leg. Could you please show work. Thankyou

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Question 978490: one leg of the right traingle is 5 iches longer than the other leg. if the hypotenuse measures 25 inches, find the length of each leg. Could you please show work. Thankyou
Answer by Cromlix(4381) (Show Source):
You can put this solution on YOUR website!
Hi there,
Make the 'other leg' = 'x'
So, the 'one leg' = x + 5
Now by Pythagoras the sum of the square of the
hypotenuse = the sum of the squares of the other
two sides.
x^2 + (x + 5)^2 = 25^2
Multiply out
x^2 + x^2 + 10x + 25 = 625
Collect like terms
2x^2 + 10x + 25 - 625 = 0
2x^2 + 10x - 600 = 0
Divide by 2 through out
x^2 + 5x - 300 = 0
Factorise
(x - 15)(x + 20) = 0
x + 20 = 0
x = -20 (no answer as -ve)
...........
x - 15 = 0
x = 15
Size of legs:
'Other leg' = 15 inches
the 'One leg' = 20 inches
Hypotenuse = 25 inches
15^2 + 20^2 = 25^2
225 + 400 = 625
625 = 625
Hope this helps:-)