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.

correction..:

how would you solve this equation?

the height of a triangle is 2m more than the base. The area is 17.5m^2. Find the length of the base.

it's height.. not measurement..

(1/2) b h = 17.5

(1/2) b (b+2) = 17.5
b^2 + 2 b = 35
b^2 + 2 b - 35 = 0
(b - 5)(b+7) = 0
b = 5
h = 7

To solve this equation, let's first denote the length of the base as "x" (in meters).

Given that the measurement of the triangle is 2 meters more than the base, we can express the length of the other side as "x + 2" (in meters).

The formula for the area of a triangle is: Area = (1/2) * base * height.

Here we have the area given as 17.5 m², so we can set up the equation:

17.5 = (1/2) * x * (x + 2)

Now, let's solve this equation step-by-step:

Step 1: Distribute (1/2) to the terms inside the parentheses:
17.5 = (1/2) * (x² + 2x)

Step 2: Simplify the expression:
17.5 = (1/2) * x² + x

Step 3: Multiply both sides of the equation by 2 to remove the fraction:
35 = x² + 2x

Step 4: Rearrange the equation to set it equal to zero:
x² + 2x - 35 = 0

Step 5: Now, we have a quadratic equation in standard form. To solve it, we can either factor or use the quadratic formula. In this case, let's use factoring, if possible.

The quadratic expression can be factored as:
(x + 7)(x - 5) = 0

Step 6: Set each factor equal to zero and solve for x:
x + 7 = 0 or x - 5 = 0

For x + 7 = 0, solving for x gives: x = -7
For x - 5 = 0, solving for x gives: x = 5

Since we are looking for the length of the base, x cannot be negative. Therefore, the solution is x = 5.

So, the length of the base of the triangle is 5 meters.

To solve this equation, we can use the formula for the area of a triangle, which is given by:

Area = (1/2) * base * height

Let's break down the problem step by step:

Step 1: Set up the equation
The problem states that the measurement of the triangle is 2m more than the base. So, let's represent the base as "x" in meters. Therefore, the measurement of the triangle would be "x + 2" meters.

We also know that the area of the triangle is 17.5 m^2. Hence, we can set up the equation as follows:

17.5 = (1/2) * x * (x + 2)

Step 2: Simplify the equation
Now, let's simplify the equation and get rid of the fraction by multiplying both sides of the equation by 2:

17.5 * 2 = x * (x + 2)

35 = x^2 + 2x

Step 3: Rearrange the equation
To solve for "x" in this quadratic equation, we need to rearrange it to quadratic form:

x^2 + 2x - 35 = 0

Step 4: Solve the quadratic equation
Now, we can solve the quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring to solve for "x":

(x + 7)(x - 5) = 0

This means that either (x + 7) equals zero or (x - 5) equals zero.

So, x + 7 = 0, or x - 5 = 0

If we solve each of these equations, we get:

x = -7, or x = 5

Step 5: Interpret the solution
Since we are talking about the length, the base cannot be negative. Therefore, we discard the solution x = -7.

Hence, the length of the base of the triangle is x = 5 meters.

Therefore, the length of the base is 5 meters.