hypotenuse (h) = 17 cm
using area of a triangle formula to solve for x
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
[tex]\frac{1}{2}[/tex] × 5x(3x - 1 ) =60 ( multiply through by 2 )
5x(3x - 1)=120
15x² - 5x - 120 = 0 ← in standard form ( divide all terms by 5 )
3x² - x - 24 = 0
consider the factors of the product 3 × - 24 = - 72 which sum to - 1
The factors are - 9 and + 8 ( split the middle term using these factors )
3x² - 9x + 8x - 24 = 0 ( factor by grouping )
3x(x - 3) + 8(x - 3) = 0 ( take out common factor (x - 3) )
(x - 3 )(3x + 8) = 0 ( equate each factor to zero and solve for x )
x - 3 = 0 ⇒ x = 3
3x + 8 = 0 ⇒ x = - [tex]\frac{8}{3}[/tex]
x > 0 ⇒ x = 3
the sides are 5x = 15 and 3x - 1 = 8
h = √(15² + 8² ) = √(225 + 64 ) = 17 ← ( hypotenuse )
