The side of a rectangular floor are xmeter and (x+7) meter. The diagonal is (x+8) meter. Calculate the value of x
Pythagoras.
x^2 + (x+7)^2 = (x+8)^2
x^2 + x^2 + 14x + 49 = x^2 + 16x + 64
x^2 - 2x - 15 = 0
(x - 5)(x + 3) = 0
x = 5 or x = -3, but a side can't be negative,
so x = 5
diagonal = √ ( first side² + second side² )
d = diagonal
first side = x + 7
second side = y
d = √ [ ( x + 7)² + y² ] = x + 8
√ ( x² + 2 • x • 7 + 7² + y² )= x + 8
√ ( x² + 14 x + 49 + y² )= x + 8
Rise both sides to the power of two.
x² + 14 x + 49 + y² = ( x + 8 )²
x² + 14 x + 49 + y² = x² + 2 • x • 8 + 8²
x² + 14 x + 49 + y² = x² + 16 x + 64
Subtract x² to both sides.
14 x + 49 + y² = 16 x + 64
Subtract 14x to both sides
49 + y² = 2 x + 64
Subtract 49 to both sides.
y² = 2 x + 15
y = √ ( 2 x + 15 )