Answer:
Base: 10 ft
Height: 2 ft
Step-by-step explanation:
We are given that a triangle has an area of 10 ft².
We know that the base of the triangle is 8 more than its height.
Since we don't know the value of the base or the height, we can say that the height is x.
Because we were given that the base is 8 more than the height, the base is 8 + x.
We need to find what the base and the height are (their values).
Recall that the area of a triangle is [tex]\frac{bh}{2}[/tex], where b is the base and h is the height.
Since we know that the base and height are x + 8 and x respectively, the area will be:
[tex]\frac{x(x+8)}{2}[/tex]
We know this value is equal to 10 (feet).
Hence,
[tex]\frac{x(x+8)}{2}= 10[/tex]
Now, we must simplify.
Multiply both sides by 2.
x(x+8) = 20
Do the distributive property on the left.
x² + 8x = 20
Subtract 20 from the right side.
x² + 8x - 20 = 0
Now, we can factor.
Think: what are 2 numbers that add up to 8, but multiply to -20?
Those numbers are 10 and -2.
Factor:
(x+10)(x-2) = 0
Split and solve:
x + 10 = 0
x = -10
x-2 = 0
x = 2
Our answers are x = 2 and x = -10. However, we must disregard x = -10, since distance cannot be negative.
This means x is 2.
Because the height is x, the height is 2 ft.
The base is therefore x + 8, or 2 + 8 = 10 ft.
