Question

instructions
solve the following problem and select your answer from the choices given.

question

the area of the triangle above is 21. what is the value of ( x )?
( \bigcirc 3 )
( \bigcirc 6 )
( \bigcirc 7 )
( \bigcirc 11 )

Explanation:

Step1: Recall triangle area formula

The area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$. Here, base = $x+1$, height = $x$, area = 21.

Step2: Substitute values into formula

$\frac{1}{2} \times (x+1) \times x = 21$

Step3: Simplify the equation

Multiply both sides by 2: $x(x+1) = 42$
Expand: $x^2 + x - 42 = 0$

Step4: Factor the quadratic equation

$(x+7)(x-6) = 0$

Step5: Solve for x

Solutions are $x=-7$ or $x=6$. Since length cannot be negative, $x=6$.

Answer:

6