Question

the area of the four walls of a room is 156 metre square the breadth and height of a room are 8 metre and 6 metre respectively find the length of the room

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Answer 1

AnswEr :

• Cuboidal Room, and Area of Four Walls i.e. CSA = 156 metre²
• Breadth of Room = 8 metre
• Height of Room = 6 metre
• Find the Length of Room?

• Curved Surface Area of the Room :

$\implies \tt CSA = 2(Length +Breadth) \times Height \\ \\\implies \tt 156 \:{m}^{2} = 2 \times (Length +8 \:m) \times 6 \:m \\ \\\implies \tt 156 \:{m}^{2} = (Length + 8 \:m) \times 12 \:m \\ \\ \implies \tt \cancel\dfrac{156 \: {m}^{2} }{12 \:m} = (Length + 8 \:m) \\ \\\implies \tt 13 \:m= (Length + 8 \:m) \\ \\\implies \tt (13 - 8)\:m= Length \\ \\\implies \boxed{\red{\tt Length = 5 \:metre}}$

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∴ Hence, Length of the Room is 5 metre.

$\rule{200}{1}$

• V E R I F I C A T I O N :

↠ CSA = 2(Length + Breadth) × Height

↠ 156 m² = 2(5m + 8m) × 6m

↠ 156 m² = 2 × 13m × 6m

↠ 156 m² = 156 m² ⠀⠀⠀Hence, Verified!

Answer 2

Answer:

$\mathbb\red{Length=5\:m}$

________________________

Given:-

Area of 4 walls = 156 sq.m

Breadth = 8 m

Height = 6 m

Length= ?

_______________________

Area =2( Length + Breadth)×Height

$\mapsto$ 156= 2(Length+8) × 6

$\mapsto$ 156 = 12(Length+8)

$\mapsto$ Length + 8 = 156/12

$\mapsto$ Length + 8 = 13

$\mapsto$ Length = (13 - 8) m

$\longmapsto$Length = 5 m

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$\therefore$ Length of the room = 5 m

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