The height of a triangle is 9m less than its base. the area of the triangle is 56 m^2 find the length of the base (show steps)

Hey there :)

We know the area formula of a triangle


We are given:
The area = 56 m²
The base = let p represent this
The height = 9 m less than the base = p - 9

Apply the formula
56 =  × ( p ) × ( p - 9 )
56 =  × ( p² - 9p )

Divide  on both sides
56 ÷ = p² - 9p
112 = p² - 9p

Bring 112 to the other side and equate equation to 0
p² - 9p - 112

Factorise { Sum = -9 , Product = - 112 , therefore suitable factors = - 16 × 7 )
( p - 16 )( p + 7 ) = 0
     ↓          ↓
 p = 16    p = - 7  ←  Reject p = - 7 since length cannot be negative

So, the length  of the base is 16 m

Check:
56 m² =  × 16 × ( 16 - 9 )
56 m² = 8 × 7
56 m² = 56 m²