Hey there :)

We know the area formula of a triangle
$\frac{1}{2} (base)(height)$

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 = $\frac{1}{2}$ × ( p ) × ( p - 9 )
56 = $\frac{1}{2}$ × ( p² - 9p )

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

7 0

3 years ago

the average lifespan of a horse is 40 years, which is five times longer than the average lifespan of a guinea pig. Use the bar d

polet [3.4K]

All you have to do is divide 40 by five and you've got your answer. I don't have the required diagram, but that would basically mean that the average lifespan of a guinea pig is about eight years, which is being generous in reality (they usually live for about 4-8 years in real life).

3 0

3 years ago