To find: A function that models area of an isoceles triangle.

e1s2kat26 2021-09-12 Answered
To find:
A function that models area of an isoceles triangle.
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Expert Answer

bahaistag
Answered 2021-09-13 Author has 101 answers

The model we want is a function that gives the area of an isosceles triangle.
Let x be the length of two equal sides of an isosceles triangle and b is given the length of its base.
Because of the perimeter of the triangle is the sum of all sides and it is 8.
Therefore, 2x+b=8
Subtract b from both sides,
2x=8b
Divide by 2,
x=8b2
Let h be the length of the altitude to the base.
h=x2(b2)2
Substitute x=8b2 in h=x2(b2)2
h=(8b2)2(b2)2
=6416b+b2b24
=6416b4
=16(4b)4
=4(4b)
=24b
Therefore, the area A of the isosceles triangle is given by
A=12bh
A(b)=12b(24b)
=b4b,0<b<4
Thus, the area A of the isosceles triangle modeled by the function
A(b)=b4b,0<b<4.
Final statement:
The area of the isosceles triangle modeled by the function
A(b)=b4b,0<b<4.

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