Question

answer fastest nd correct ​

Answer 1

1)

$\huge{\underline{\textbf{Given:-}}}$

• Ratio if Adjacent sides if Rectangle = 5:12
• Perimeter of Rectangle

$\huge{\underline{\textbf{Find:-}}}$

• Length of smaller side.

$\huge{\underline{\textbf{Solution:-}}}$

Let, Length of Rectangle = 5x cm

Breadth of Rectangle = 12x cm

Now, by using

$\underline{\boxed{\sf Perimeter \: of \: Rectangle = 2(l + b)}}$

$\sf where \small{\begin{cases} \sf Perimeter = 34cm \\ \sf l = 5x \:cm\\ \sf b = 12x \: cm\end{cases}}$

Substituting these values:-

$\implies\sf Perimeter \: of \: Rectangle = 2(l + b)$

$\implies\sf 34= 2(5x+12x)$

$\implies\sf 34= 2(17x)$

$\implies\sf 34= 34x$

$\implies\sf \dfrac{34}{34}= x$

$\implies\sf 1cm= x$

Now, Smaller Side:-

> Smaller Side, Length = 5x

> 5×1 = 5cm

$\underline{\boxed{\sf \therefore Smaller \: Side \: of \: Rectangle \:is \: 5cm}}$

Hence, Option (c) 5cm is correct.

____________________________

2)

$\huge{\underline{\textbf{Given:-}}}$

• Same as above question.

$\huge{\underline{\textbf{Find:-}}}$

• Length of Diagonal.

$\huge{\underline{\textbf{Solution:-}}}$

Here, Length = 5cm [finded above]

Breadth = 12x = 12×1 = 12cm [as x = 1cm]

Now, we know that diagonal of rectangle:-

$\huge{\underline{\boxed{\sf d^2 = l^2 + b^2}}}$

$\sf where \small{\begin{cases} \sf l = 5cm\\ \sf b = 12cm\end{cases}}$

Substituting these values:-

$\dashrightarrow\sf d^2 = l^2 + b^2$

$\dashrightarrow\sf d^2 = 5^2 + 12^2$

$\dashrightarrow\sf d^2 = 25 + 144$

$\dashrightarrow\sf d^2 = 169$

$\dashrightarrow\sf d= \sqrt{169}$

$\dashrightarrow\sf d= 13cm$

$\underline{\boxed{\sf \therefore Diagonal \: of \: Rectangle \:is \: 13cm}}$

Hence, Option (c) 13cm is correct.