Respuesta :
Given:
There are given that the height of a triangle is 6 cm longer than its base.
Explanation:
According to the question.
We need to find the length of the base and the height.
So,
Suppose the height of the triangle is H and the base of the triangle
According to the given data:
[tex]H=B+6[/tex]Then,
From the area of the triangle:
[tex]A=\frac{1}{2}(B\times H)[/tex]Then,
Put all the value into the give formula:
So,
[tex]\begin{gathered} A=\frac{1}{2}(B\times H) \\ 36\times2=\frac{1}{2}\times2\times B(B+6) \\ B^2+6B=72 \end{gathered}[/tex]Then,
[tex]\begin{gathered} B^{2}+6B=72 \\ B^2+6B-72=72-72 \\ B^2+6B-72=0 \end{gathered}[/tex]Then,
[tex]\begin{gathered} B^{2}+6B-72=0 \\ (B+12)(B-6)=0 \\ B=-12;B=6 \end{gathered}[/tex]Then,
According to the concept, the value of the base cannot be negative.
So,
The value of the base is:
[tex]B=6[/tex]Now,
From the give statement:
[tex]\begin{gathered} H=B+6 \\ H=6+6 \\ H=12 \end{gathered}[/tex]Final answer:
Hence, the base of the triangle is 6 and the height of the triangle is 12.
