Respuesta :
The amount of material needed by Marta to make the flag is;
[tex]\rm Area =\sqrt{50(50-d_1)(50-d_2)(50-d_3)}[/tex] square inch.
The total cost of making the flag is;
[tex]\rm 0.15 \times\rm \sqrt{50(50-d_1)(50-d_2)(50-d_3)}[/tex] dollar.
Given
Marta is making a flag with the given dimensions.
The perimeter of the flag is 100 inches.
Let us consider that the flag has a triangular shape.
Hero's formula;
According to the Hero's formula;
The area of the triangle is given by;
[tex]\rm Area =\sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where, s is the semi perimeter and a, b, and c are the sides of the triangle.
Semi perimeter s = P/2,
Since the perimeter of the flag is 100 inches.
[tex]\rm S=\dfrac{100}{2}\\\\S=50[/tex]
The dimensions of triangular shape are [tex]\rm d_1, d_2 \ and \ d_3[/tex].
Then,
The area of the triangular flag becomes;
[tex]\rm Area =\sqrt{s(s-a)(s-b)(s-c)}\\\\\rm Area =\sqrt{50(50-d_1)(50-d_2)(50-d_3)}[/tex]
So the amount of material needed to make the flag is;
[tex]\rm Area =\sqrt{50(50-d_1)(50-d_2)(50-d_3)}[/tex]
Therefore,
The cost of material = C = $0.15 per square inch
So the total cost in making the flag will be;
[tex]\rm C\times A=0.15 \times A\\\\=0.15 \times\rm \sqrt{50(50-d_1)(50-d_2)(50-d_3)}[/tex].
Hence, The amount of material needed by Marta to make the flag is [tex]\rm Area =\sqrt{50(50-d_1)(50-d_2)(50-d_3)}[/tex].
To know more about Hero's formula click the link given below.
https://brainly.com/question/24399817
