Question

If the sum of the diagonals of a rectangle is 26 cm and one of its side is 5 cm, then find the
length of other sides and both diagonals.


Please Tell The Correct Answer!
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Answer 1

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Given :-

• A rectangle ABCD with diagonals AC and BD.
• Let BC = AD = 5 cm (Opposite sides of a rectangle are equal)
• AC + BD = 26 cm (Sum of both diagonal)

To Find :-

• Length of AB and DC (Other sides)
• Length of Diagonal

Solution :-

Let the measure of each diagonal be 'x cm'.

Also, we know that both the diagonals of the rectangle are equal, therefore,

AC + BD = 26 cm (Sum of both diagonal)

AC + BD = x + x = 26 cm

2x = 26 cm

x = 26/2 cm

x = 13 cm

• AC = BD = 13 cm

$\boxed{ \sf{\therefore \: Length \: of \: diagonal \: = \: 13 \: cm}}$

To Find the length of the other side of the rectangle, Using Pythagoras Theorem in triangle ABC :

$\sf{ {hyp}^{2} = {opp}^{2} + {adj}^{2} } \\ \: \sf{{AC }^{2} = { BC }^{2} } + { AB}^{2} \\ \sf{{13 }^{2} = { 5}^{2} } + { AB}^{2} \\ \sf{{ AB}^{2} = 169 - 25} \\ \sf{{ AB}^{2} = 144} \\ \sf{AB = \sqrt{144} } \\ \boxed{ \therefore\sf{AB= DC = 12cm}}$

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