Question

The area of four walls of a room is 150 ^2 m . If the length of the room is twice its breadth and the height is 4 m, find the area of the floor .​ ​

Answer 1

Answer:

Given :

Area of four walls of a room = 150 m²

Height of the room = 4 m

Length of the room is twice the breadth of the room

To Find :

The Area of the floor

Solution :

Let the breadth of the room be "b" . Then the length of thr room becomes "2b' [Given condition]

Area of Four walls of a room is given by ,

$\\ \star \: {\boxed{\purple{\sf{Area_{(four \: walls)} = 2(length + breadth) \times height}}}}$

Substituting the values we have ,

$\\ : \implies \sf \: 150 = 2(2b + b) \times 4$

$\\ : \implies \sf \: 150 = 2(3b) \times 4$

$\\ : \implies \sf \: 150 = 6b \times 4$

$\\ : \implies \sf \: 6b = \frac{150}{4}$

$\\ : \implies \sf \: 6b = 37.5$

$\\ : \implies \sf \: b = \frac{37.5}{6}$

$\\ : \implies{\underline{\boxed{\blue{\mathfrak{b = 6.25 \: cm}}}}}$

So , The Breadth of the room is 6.25 cm. The the length of the room is 2(6.25) which is equal to 12.5 cm.

$\qquad$━━━━━━━━━━━━━━━

Area of floor is given by ,

$\\ \star \: {\boxed{\purple{\sf{Area_{(floor)} = length \times width}}}}$

Substituting the values we have ,

$\\ : \implies \sf \: Area_{(floor)} = 12.5 \times 6.25$

$\\ : \implies{\underline{\boxed {\pink{\mathfrak{Area_{(floor)} = 78.125 \: {cm}^{2} }}}}} \: \bigstar$

$\\ \therefore \: {\underline{\sf{Hence \: , \: The \: Area \: of \: the \: Floor \: is \: \bold{78.125 cm^2}}}}$

Answer 2

Answer:

Given :

Area of four walls of a room = 150 m²

Height of the room = 4 m

Length of the room is twice the breadth of the room

To Find :

The Area of the floor

Solution :

Let the breadth of the room be "b" . Then the length of thr room becomes "2b' [Given condition]

Area of Four walls of a room is given by ,

$\\ \star \: {\boxed{\purple{\sf{Area_{(four \: walls)} = 2(length + breadth) \times height}}}}$

Substituting the values we have ,

$\\ : \implies \sf \: 150 = 2(2b + b) \times 4$

$\\ : \implies \sf \: 150 = 2(3b) \times 4$

$\\ : \implies \sf \: 150 = 6b \times 4$

$\\ : \implies \sf \: 6b = \frac{150}{4}$

$\\ : \implies \sf \: 6b = 37.5$

$\\ : \implies \sf \: b = \frac{37.5}{6}$

$\\ : \implies{\underline{\boxed{\blue{\mathfrak{b = 6.25 \: cm}}}}}$

So , The Breadth of the room is 6.25 cm. The the length of the room is 2(6.25) which is equal to 12.5 cm.

$\qquad$━━━━━━━━━━━━━━━

Area of floor is given by ,

$\\ \star \: {\boxed{\purple{\sf{Area_{(floor)} = length \times width}}}}$

Substituting the values we have ,

$\\ : \implies \sf \: Area_{(floor)} = 12.5 \times 6.25$

$\\ : \implies{\underline{\boxed {\pink{\mathfrak{Area_{(floor)} = 78.125 \: {cm}^{2} }}}}} \: \bigstar$

$\\ \therefore \: {\underline{\sf{Hence \: , \: The \: Area \: of \: the \: Floor \: is \: \bold{78.125 cm^2}}}}$