Question

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)

Answer 1

Hey there :)

We know the area formula of a triangle

`(1)/(2) (base)(height)`

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 =
`(1)/(2)` × ( p ) × ( p - 9 )
56 =
`(1)/(2)` × ( p² - 9p )

Divide
`(1)/(2)` on both sides
56 ÷
`(1)/(2)` = 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 =
`(1)/(2)` × 16 × ( 16 - 9 )
56 m² = 8 × 7
56 m² = 56 m²