Question

The sides of a pair of adjacent sides of a rectangle are in the ratio 3:4 if its diagonal is 20cm long then find the lengths of the sides and heance the perimeter of the rectangle

Answer 1

$\huge\bold{ANSWER~:}$

• Here ratio of length and breath is 3:4.

• We know that each angle of rectangle is right angle and diagonal is hypotenuse and length and breath are two sides.

${(20)}^{2} = {(3x)}^{2} + {(4x)}^{2} \\ \\ 400 = 9 {x}^{2} + 16 {x}^{2} \\ \\ 400 = 25 {x}^{2} \\ \\ \frac{400}{25} = {x}^{2} \\ \\ 16 = {x}^{2} \\ \\ x = 4 \: cm$

• Length = 3x = 12 cm

• Breath = 4x = 16 cm

We know that perimeter of rectangle :-

• 2(l+b)

$= 2(16 + 12) \:cm \\ \\ = 56 \: cm$

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