The value of 'x' is 6 and this can be determined by using the formula of the area of the triangle and the factorization method.
Given :
The area of the triangle above is 21.
The following steps can be used in order to determine the value of 'x':
- Step 1 - The formula of the area of a triangle is used in order to determine the value of 'x'.
- Step 2 - The formula of triangle area is given below:
[tex]A = \dfrac{1}{2}\times B \times H[/tex]
where B is the base and H is the height of the triangle.
- Step 3 - Now, substitute the value of A, H, and B in the above formula.
[tex]21 = \dfrac{1}{2}\times (x+1) \times x[/tex]
- Step 4 - Simplify the above expression.
[tex]42 = x^2+x[/tex]
[tex]x^2+x-42=0[/tex]
- Step 5 - Factorize the above quadratic equation.
[tex]x^2+7x-6x-42=0[/tex]
[tex]x(x+7)-6(x+7)=0[/tex]
[tex](x-6)(x+7)=0[/tex]
- Step 6 - The length is never negative. So, the value of 'x' is 6.
For more information, refer to the link given below:
https://brainly.com/question/15442893
