Question

2. A mirror of length 40 cm and width 20 cm is to be framed with a 4 cm wide frame. Find the area of
the frame required .a also find the cost of framing at the rate of Rs. 157 cm?​

Answer 1

Step-by-step explanation:

this is the answer and process ☝️☝️☝️

Answer 2

✦ Given :

• A mirror of length 40cm and width 20cm.
• It needs to be framed. The frame of the mirror is 4cm wider than the mirror.

$\begin{gathered} {\orange{\star{\pink{\textsf{\textbf{Naming}}}}}} \begin{cases} \sf{ABCD \to \: area \: of \: the \: mirror} \\ \sf{EFGH \to area \: of \: the \: outer \: rectangle} \\ \end{cases} \end{gathered}$

❐ Step 1 :

➪ Given dimensions of the rectangular-mirror :

→ length = 40cm.

→ breadth = 20cm.

Area of the mirror ABCD is given by :

$\sf\longrightarrow area \: of \: the \: rectangle \: ABCD_{ \gray{(mirror)}} = l \times b$

We have,

l (length) = 40cm

b (breadth) = 20cm

✦ From the given dimensions :

$\sf\longrightarrow area \: of \: the \: rectangleABCD_{ \gray{(mirror)}} = (40\times 20) {cm}^{2}$

$\sf\longrightarrow area \: of \: the \: rectangleABCD_{ \gray{(mirror)}} = 800 {cm}^{2}$

❐ Step 2 :

[Following the figure]

✦ Dimensions of the outer rectangle EFGH :

→ Length = 40 + (2*4)

= 40 + 8

= 48cm.

→ Breadth = 20 + (2*4)

= 20 + 8

= 28cm.

• The mirror frame is in rectangle shape

So,

✦ Area of the outer rectangle is given by :

$\sf\longrightarrow area \: of \: the \: rectangle_{ \gray{(EFGH)}} = (48\times 28 ) {cm}^{2}$

$\sf\longrightarrow area \: of \: the \: rectangle_{ \gray{(EFGH)}} = 1344{cm}^{2}$

❐ Step 3 :

✦ Area of the frame is given by :

$\sf \to EFGH - ABCD \:$

$\begin{gathered}{\orange{\star {\pink{ \textsf{ \textbf{Here}}}}}} \begin{cases} \sf{ABCD \to \: area \: of \: the \: mirror} \\ \sf{EFGH \to area \: of \: the\: outer \: rectangle} \end{cases} \end{gathered}$

$\sf \to \: (1344 - 800) {cm}^{2}$

$\sf \to \: 544 {cm}^{2}$

❐ Step 4 :

✦ Calculate the total cost of framing the mirror:

• Rate of framing the mirror is ₹157 per cm²

$\because$ Since, 1cm² costs ₹157

$\therefore$ Then 544cm² will cost (₹157*544) = ₹85, 408

$\therefore$ The required area of the frame is 544cm² and the total cost of framing is ₹85,408.