Question

For the decoration on Yashika’s birthday, Yashika and Mansi

prepared coloured paper penants in the form of scalene

triangles in two sizes

(i) green coloured pennant of sides 3 inches,4 inches,5 inches

(ii) red coloured pennant of sides 5 inches,7 inches,8 inches

They prepared fifty pennants of each colour

Question1; Find the total red coloured paper used.

(A) 150 square inches

(B) 300 square inches

(C) 400 square inches

(D) 450 square inches

Question 2 : Find the total green coloured paper used.

(A) 465 square inches

(B) 550 square inches

(C) 866 square inches

(D) 666 square inches

Question 3: If each coloured paper sheet is available in the size

of 24 inches × 24 inches, what is the minimum

number of sheets required of each colour?

(A) 1 green, 3 red

(B) 2 green, 2 red

(C) 1 green, 2 red

(D) 3 green, 3 red​

Answer 1

question 1 answer :

C)

question 2 answer :

A)

question 3 answer :

B)

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Answer 2

Answer:

• The total red colored paper used is  $17.32\hspace{.1cm}inches^{2}$.
• The total green colored paper used is $300 \hspace{.1cm}inches^{2}$.
• $1$ sheet of green color and $2$ sheets of red color

Step-by-step explanation:

Given,

Red-colored pennant :    a =  $5$ inches, b = $7$ inches, c = $8$ inches

Green colored pennant : a = $3$ inches, b = $4$ inches, c= $5$ inches

Step 1:

For red-colored pennant :

$s=\frac{a+b+c}{2}$             $\implies$     $s=\frac{5+7+8}{2}$   $=10$

area of a pennant   =   $\sqrt{s(s-a)(s-b)(s-c)}$

                                =  $\sqrt{10(10-5)(10-7)(10-8)}$

                                =  $\sqrt{10\times 5\times 3 \times 8}$

                                = $17.32\hspace{.1cm}inches^{2}$

Area of $50$ pennants =   $17.32\times 50$

                                  =   $866 \hspace{.1cm}inches^{2}$

$\therefore$  The total red colored paper used is  $17.32\hspace{.1cm}inches^{2}$.

       

Step 2:

For green-colored pennant :

$s=\frac{a+b+c}{2}$             $\implies$     $s=\frac{3+4+5}{2}$   $=6$

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

                                =  $\sqrt{6(6-3)(6-4)(6-5)}$

                                =  $\sqrt{10\times 5\times 3 \times 8}$

                                = $6\hspace{.1cm}inches^{2}$

Area of $50$ pennants =   $6\times 50$

                                  =   $300 \hspace{.1cm}inches^{2}$

$\therefore$  The total green colored paper used is $300 \hspace{.1cm}inches^{2}$.

Step 3:

Since the size of the sheet is $24 inches \times 24 inches$ , its area will be

$576$ $inches^{2}$ .

We know that red-colored used is $866$ $inches^{2}$ which is more than the available sheet.  Hence , we require $2$ sheets of red color.

The green color sheet used is $300$ $inches^{2}$ which is less than the already available sheet of  $576$ $inches^{2}$.  Hence, we require only $1$ sheet of green color.

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