Question

The side of a rectangular floor are xmeter and (x+7) meter. The diagonal is (x+8) meter. Calculate the value of x

Answer 1

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

Answer 2

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 )