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?

○ 3
○ 6
○ 7
○ 11

Explanation:

Step1: Recall triangle area formula

Area = $\frac{1}{2} \times base \times height$

Step2: Substitute given values

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

Step3: Simplify equation

$42 = x(x+1) \Rightarrow x^2 + x - 42 = 0$

Step4: Solve quadratic equation

Factor: $(x+7)(x-6)=0 \Rightarrow x=6$ (since length>0)

Answer:

6