The height of a triangle is 4 m less than its base the area of the triangle is 48 m² find the length of its base

Question

please help?  Thank you!!!!! 

Answer 1

To solve this problem you need to know the formula for finding the area of a triangle:

• A = ½·b·h

 

Or in words:

• "The area of a triangle is half of its base times its height."

 

In this case we know neither the base nor the height of the triangle, but we do know how they are related (i.e. The height of the triangle is 4m less than its base). We can write one unknown value in terms of the other then. We know that the two values are 4 apart, with height being the smaller of the two values. We could express this two ways:

• height = base - 4
• base = height + 4

 

Both of these express the same fact. I personally prefer using expression with addition, but either will work. We abbreviate the expression to:

• h = b - 4

This allows us to substitute and rewrite the original formula as:

• A = ½·b·h → A = ½·b·(b - 4)
  

We also know from the problem itself that the area is 48 m². So we can include that too:

• A = ½·b·(b - 4) → 48 = ½·b·(b - 4)

Now we have an equation with a single variable which can be solved using algebra:

• b² - 4b - 96 = 0 → (quadratic formula or observation) → b = 12 or -8

Since -8 doesn't make any sense as a possible length, we conclude that b is 12. In words,

• "The length of the base of the triangle is 12 meters."

Answer 2

Let x = base measurement; then height = (x-4).

 

A = ½•base•height =

 

48 = ½x(x-4).  A quadratic equation that you should be able to solve.