Question

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? $.

Answer 1

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

$\rm Area =\sqrt{50(50-d_1)(50-d_2)(50-d_3)}$ square inch.

The total cost of making the flag is;

$\rm 0.15 \times\rm \sqrt{50(50-d_1)(50-d_2)(50-d_3)}$ 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;

$\rm Area =\sqrt{s(s-a)(s-b)(s-c)}$

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.

$\rm S=\dfrac{100}{2}\\\\S=50$

The dimensions of triangular shape are $\rm d_1, d_2 \ and \ d_3$.

Then,

The area of the triangular flag becomes;

$\rm Area =\sqrt{s(s-a)(s-b)(s-c)}\\\\\rm Area =\sqrt{50(50-d_1)(50-d_2)(50-d_3)}$

So the amount of material needed to make the flag is;

$\rm Area =\sqrt{50(50-d_1)(50-d_2)(50-d_3)}$

Therefore,

The cost of material = C = $0.15 per square inch

So the total cost in making the flag will be;

$\rm C\times A=0.15 \times A\\\\=0.15 \times\rm \sqrt{50(50-d_1)(50-d_2)(50-d_3)}$.

Hence, The amount of material needed by Marta to make the flag is $\rm Area =\sqrt{50(50-d_1)(50-d_2)(50-d_3)}$.

To know more about Hero's formula click the link given below.

brainly.com/question/24399817