Answer:
The value of x is 8cm. The length of 3 sides are 8cm, 15cm and 17cm.
Explanation:
Using Pythagoras' Theorem, a²+b² = c² :
Let a be x cm,
Let b be x+7 cm,
Let c be 2x+1 cm
x² + (x+7)² = (2x+1)²
x² + x² + 14x + 49 = 4x² + 4x + 1
2x² + 14x + 49 = 4x² + 4x + 1
Then, move all the variables to one side and solve it to find the value of x :
4x² + 4x + 1 - 2x² - 14x - 49 = 0
2x² - 10x - 48 = 0
2(x² - 5x - 24) = 0
x² - 5x - 24 = 0
(x-8)(x+3) = 0
x - 8 = 0
x = 8 cm
x + 3 = 0
x = -3 cm (rejected)
Substitute the x value into the length of a,b and c :
a = x
= 8 cm
b = x + 7
= 8 + 7
= 15 cm
c = 2x + 1
= 2(8) + 1
= 16 + 1
= 17 cm