Question

please solve this word problem. 11. Find the length of the diagonal of a rectangle
whose sides are 15 cm and 8 cm.​

Answer 1

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

Find the length of the diagonal of a rectangle whose sides are 15 cm and 8 cm.

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{\red{Given}}}}}$

• Length of rectangle = 15 cm
• width of rectangle = 8 cm

$\Large{\underline{\mathfrak{\bf{\red{Find}}}}}$

• Length of diagonal

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

In Rectangle ABCD ,

CD is diagonal of this rectangle ,

Here,

• AB = 8 cm = CD
• BC = 15 cm = DA

we know,

$\small\boxed{\boxed{\sf{\red{\:Length_{diagonal}\:=\:\pm\sqrt{(lenght)^2+(width)^2}}}}}$

Keep value of Length and width ,

$\mapsto\sf{\:Length_{diagonal}\:=\:\pm\sqrt{(15)^2+(8)^2}} \\ \\ \\ \mapsto\sf{\:Length_{diagonal}\:=\:\pm\sqrt{225+64}} \\ \\ \\ \mapsto\sf{\:Length_{diagonal}\:=\:\pm\sqrt{289}} \\ \\ \\ \mapsto\sf{\:Length_{diagonal}\:=\:\pm\:17}$

But, we know, length always be positive .

So, neglect negative (-ve)sign ,

And, Take positive (+ve) sign .

$\mapsto\sf{\orange{\:Length_{diagonal}\:=\:\:17\:cm}}$

$\Large{\underline{\mathfrak{\bf{\green{Hence}}}}}$

• Length of diagonal of rectangle = 17 cm

Answer 2

Given :

• Sides of the rectangle are 15 cm and 8 cm.

To find :

• Diagonal of the rectangle =?

Step-by-step explanation:

Sides of the rectangle are 15 cm and 8 cm. [Given]

We know that,

Diagonal of Rectangle =

_______________

√lenght²+breadth ²

Substituting the values in the above formula, we get,

__________

Diagonal = √ ( 15) ² + ( 8) ²

__________

Diagonal = √ 225 + 64

______

Diagonal = √ 289

______

Diagonal = √ 17 × 17

Diagonal = 17

Thus, The Diagonal of the rectangle = 17 cm.

Formula related to the rectangle :

• Area of rectangle = length × breadth.

• Perimeter of rectangle = 2 ( lenght + Breadth)

• Diagonal of rectangle = √( l² + b² )