Answer:
The base is 10cm and the height is 20cm.
Explanation:
Let's start with the base. We don't know what it is. Because I do not like using b as a variable, let's use x.
x = base
Huh, we don't know the height either. But we know it is 10cm longer than the base.
h = x + 10
Also we know the area of the triangle, 100cm^2.
Use the area formula for a triangle:
A = 1/2bh
Fill in what we know.
100 = 1/2(x)(x + 10)
Times by 2 to just rid ourselves of fractions.
200 = x(x + 10)
Use distributive property.
200 = x^2 + 10x
subtract 200
0 = x^2 + 10x - 200
Factor.
0 = (x + 20)(x - 10)
Use Zero Product Property (this just means set each factor equal to zero)
x + 20 = 0 and x - 10 = 0
for x + 20 = 0,
subtract 20
x = -20
We'll trash this answer because lengths cannot be negative.
For the second equation, x - 10 = 0
add 10
x = 10
Remember x is the base. So the base is 10cm.
The height is 10cm longer, so the height is 20cm.
Check: if
base = 10
height = 20
Area = 1/2bh
Area = 1/2(10)(20)
Area = 100 check!
The base is 10cm and the height is 20cm.