how would you solve this equation?
the measurement of a triangle is 2m more than the base. The area is 17.5m^2. Find the length of the base.
To solve this equation, we need to set up an equation based on the given information and then solve for the unknown variable, which is the length of the base.
Let's analyze the information provided:
1. The measurement of the triangle is 2m more than the base.
Let's represent the length of the base as 'x'. Therefore, the measurement of the triangle would be 'x + 2'.
2. The area of the triangle is 17.5m^2.
The formula for calculating the area of a triangle is (1/2) * base * height. In this case, the base is represented by 'x' and the height by 'x + 2'. So we can set up the equation: (1/2) * x * (x + 2) = 17.5.
Now we can solve the equation step by step:
Step 1: Distribute the (1/2) to the expression (x + 2):
(1/2) * x^2 + (1/2) * 2x = 17.5
Step 2: Simplify the equation:
(1/2) * x^2 + x = 17.5
Step 3: Multiply each term of the equation by 2 to remove the fraction:
x^2 + 2x = 35
Step 4: Rearrange the equation to have all terms on one side:
x^2 + 2x - 35 = 0
Step 5: Factor or use the quadratic formula to solve the equation.
In this case, the equation factors as (x - 5)(x + 7) = 0.
So, either x - 5 = 0 or x + 7 = 0.
Step 6: Solve for x:
If x - 5 = 0, then x = 5.
If x + 7 = 0, then x = -7.
Since the length cannot be negative in this context, the length of the base of the triangle is 5m.
Therefore, the length of the base is 5m.