Question

Please help on this pythagorean question, find x.

Answer 1

x = 4

Explanation:

Since the triangle is right use Pythagoras' identity to solve for x

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

(x + 3)² + (4(x + 2))² = 25² ← expand parenthesis on left side

x² + 6x + 9 + 16(x+ 2)² = 625

x² + 6x + 9 + 16(x² + 4x + 4) = 625

x² + 6x + 9 + 16x² + 64x + 64 = 625 ← simplify left side

17x² + 70x + 73 = 625 ( subtract 625 from both sides )

17x² + 70x - 552 = 0 ← in standard form

with a = 17, b = 70, c = - 552

Using the quadratic formula to solve for x

x = ( - 70 ±
`√(70^2-(4(17)(-552))` ) / 34

= ( - 70 ±
`√(4900+37536)` ) / 34

= - 70 ±
`√(42436)` ) / 34

= - 70 ± 206 ) / 34

x =
`(-70-206)/(34)` = - 8.1176....

or x =
`(-70+206)/(34)` = 4

However, x > 0 ⇒ x = 4

Hence

x + 3 = 4 + 3 = 7 and

4(4 + 2) = 24

The triangle is a 7- 24- 25 right triangle