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)

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16-04-2018
Mathematics

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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)

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penfila11Pen penfila11Pen · Answer 1 · 2018-04-16T10:01:43+02:00

Hey there :)

We know the area formula of a triangle
[tex] \frac{1}{2} (base)(height)[/tex]

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 = [tex] \frac{1}{2} [/tex] × ( p ) × ( p - 9 )
56 = [tex] \frac{1}{2} [/tex] × ( p² - 9p )

Divide [tex] \frac{1}{2} [/tex] on both sides
56 ÷ [tex] \frac{1}{2} [/tex] = 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 = [tex] \frac{1}{2} [/tex] × 16 × ( 16 - 9 )
56 m² = 8 × 7
56 m² = 56 m²