Answer:
x = 10 and y = 24
Explanation:
Perimeter of triangle = sum of the 3 sides of the triangle
:. x + y + 26 = 60
x + y = 60 - 26
x + y = 34 ---- (1)
From Pythagoras theorem,
x² + y² = 26²
x² + y² = 676 ---- (2)
From equation (1): y = 34 - x
:. x² + (34 - x)² = 676
x² + 1,156 - 68x + x² = 676
x² + x² - 68x + 1,156 - 676 = 0
2x² - 68x + 480 = 0
x² - 34x + 240 = 0
(x² - 24x) - (10x + 240) = 0
x(x - 24) -10(x - 24) = 0
(x - 24)(x - 10) = 0
x = 24 or 10
y = 34 - x
y = 34 - 10 = 24
:. x = 10 and y = 24