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Marta is making a flag with the given dimensions. The perimeter of the flag is 100 inches. How much material, in square inches, is needed to make the flag?

?? square inches

If the material costs $0.15 per square inch, how much will Marta spend on materials to make the flag?

$??

Respuesta :

tkmaplethorpepaykzs

She would need 360 square inches of fabric, we know this by using the heron's formula P =100, S = 50

A = (50(50-41)(50-41)(50-18))^.5

A = (50(9^2)(32))^.5

A = 9(50(32))^.5

A = 9(1600)^.5

A = 9*40

A = 360



360*0.15 per piece equals $54


Answers:


360, 54

rahulsharma789888

The amount of material needed by Marta  to make the flag is

[tex]\rm \sqrt{(50)\times (d_1-50)(d_2-50)(d_3-50)}[/tex] square inch

The total cost in making the flag is

[tex]\rm 0.15\times\ \sqrt{(50)\times (d_1-50)(d_2-50)(d_3-50)}[/tex] dollars .

Marta is making a  flag with given dimensions. The perimeter of the flag is 100 inches

Let us consider that the flag has a triangular shape

According to hero's formula

The area of triangle is given by

[tex]\rm Area = A = \sqrt{s \times (s-a) (s-b) (s-c)}\\where \; s = Semi perimeter\\a, b, c \; are\; the \; sides\; of \; the\; triangle[/tex]

Let us consider that P represents the perimeter

Semi perimeter s = P/2

Since the perimeter of flag is 100 inches

so s = 100/2 = 50

Let the dimensions of triangular shape be [tex]\rm d_1, d_2 \; and\; d_3[/tex]

so Area of the triangular flag becomes

[tex]\rm A= \sqrt{(50)\times (d_1-50)(d_2-50)(d_3-50)}[/tex] square inch

So the amount of material needed to make the flag is

[tex]\rm A= \sqrt{(50)\times (d_1-50)(d_2-50)(d_3-50)}[/tex] square inch

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\ \sqrt{(50)\times (d_1-50)(d_2-50)(d_3-50)}[/tex] dollars.

For more information refer to the link below

https://brainly.com/question/12454834

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