Question

The adjacent sides of a rectangle are in the ratio 5:12 . If the perimeter of the rectangle is 34 cm. Find the diagonals of the rectangle.​

Answer 1

Answer:

Assuming -

Length = 12x

Breadth = 5x

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Solution -

$\color{black}\boxed{\colorbox{saffron}{Perimeter-2(length+breadth) }}$

34= 2(12x+5x)

34= 2×17x

34= 34x

$\cancel\frac{34}{34}$=x

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Required Answer -

$\rightarrow$length=12x= 12cm

$\rightarrow$breadth= 5x = 5cm

Answer 2

Answer:

$\frak {Given} \begin{cases} \sf \: ratio \: of \: length \: and \: breadth \: = 5 \ratio \: 12 \\ \sf \: perimeter = 34 \: cm \end{cases}$

Need to Find :-

Diagonal of rectangle

Solution :-

Let the Ratio be 5x and 12x

34 = 2(5x + 12x)

34 = 10x + 24

34 - 24 = 10x

10 = 10x

10/10 = x

1 = x

Length : 12 cm

Breadth : 5 cm

Now,

Finding Diagonal

${ \boxed{ \pink{ \underline{ \sf \: Diagonal = \sqrt{{length}^{2} + {breadth}^{2}}}}}}$

$\sf \: Diagonal = \sqrt{ {12}^{2} + {5}^{2} }$

$\sf \: Diagonal \: = \sqrt{14 4 + 25}$

$\sf \: Diagonal = \sqrt{169}$

$\sf \pink{Diagonal = 13 \: cm}$