Question

The rectangular floor of a room is 15cm long and 8cm wide. What is the length of the diagonal of the room?
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Answer 1

Given :

• Length of the rectangular floor of room = 15 cm
• Width of the rectangular floor of room = 8 cm

To Find :

• The length of diagonal of room

Solution :

The diagonal of a rectangle when it's length and breadth are given is given by ,

$\\ \star \: {\boxed{\red{\sf{(Diagonal)^2 = (Length)^2 + (width)^2}}}}$

We have ,

• Length = 15 cm
• Width = 8 cm

Substituting the values ;

$\\ : \implies \sf \:(Diagonal)^2 = {(15 \: cm)}^{2} + {(8 \: cm)}^{2}$

$\\ : \implies \sf \:(Diagonal)^2 = 225 \: {cm}^{2} + 64 \: {cm}^{2}$

$\\ : \implies \sf \:(Diagonal)^2 =289 \: {cm}^{2}$

$\\ : \implies \sf \:Diagonal = \sqrt{289 \: {cm}^{2} }$

$\\ : \implies{\underline{\boxed{\pink{\mathfrak{\: Diagonal= 17 \: cm}}}}} \: \bigstar$

Hence ,

• The length of the diagonal is 17 cm.

Answer 2

Answer:-

$\small \bf \underline{Given:}$

★★ Length of the rectangular floor of the room = 15 cm

★★ Width of the rectangular floor of the room = 8 cm

$\small \bf \underline{To \: find:}$

We need to find the length of the diagonal of the room

$\small \bf \underline{Solution:}$

To find the diagonal we use the Pythagorean Theorem :

$\bf \: c = \sqrt{ {a}^{2} + {b}^{2} }$

where

c = length of the diagonal of the room

a = length of the rectangular floor of the room

b = width of the rectangular floor of the room

Let the length of the diagonal of the room be x

After substituting the values, the equation stands as follows :

$\bf \: x = \sqrt{ {15}^{2} + {8}^{2} }$

$\bf \implies \: x = \sqrt{225 + 64}$

$\bf \implies \: x = \sqrt{289}$

$\bf \implies \: x = 17$

Answer: Length of the diagonal of the room = 17 cm

@BengaliBeauty

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