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Answer:
C
Step-by-step explanation:
That makes the third side 8 inches. Bc 34 -12 -14 = 8.
There's a formula that gives you the area of a triangle with all three sides.
It's kinda long so I won't write it out but it uses the semi-perimeter and it's called heron's formula if you want to search it up.
I just plugged the values into Heron's formula calculator.
The answer is around 47.906158268014, so C.
Area of the triangle is [tex]47.91 \ in^{2}[/tex].
The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane.
Given
Perimeter = 34
Two sides of the triangle = 12, 14
Third side of the triangle = Perimeter - 12 - 14
= 34 - 12 - 14
= 8 inches
According to the figure, using Pythagoras theorem
[tex]h^{2}=8^{2} -x^{2}[/tex]
[tex]h^{2}=12^{2} - (14-x)^{2}[/tex]
[tex]8^{2} -x^{2} =12^{2} -(14-x)^{2}[/tex]
[tex]64-x^{2} =144-196+28x-x^{2}[/tex]
[tex]28x=116[/tex]
[tex]x=4.14[/tex]
So, [tex]h^{2} =8^{2} -4.14^{2}[/tex]
[tex]h^{2} =64-17.15[/tex]
[tex]h=6.844[/tex]
So, the area of the triangle = [tex]\frac{1}{2} \times 14 \times 6.844[/tex]
= [tex]47.91 \ in^{2}[/tex]
Area of the triangle is [tex]47.91 \ in^{2}[/tex].
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