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.
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Answer 1

Answer:

Let the diagonals be d1 and d2.

We know that, d1+d2 = 26 cm.

One of the side of the rectangle is y = 5 cm.

Let the other unknown side be x.

Most Important :

In a rectangle

• All the angles = 90°
• Opposite sides are equal
• Diagonals are equal

Hence, d1=d2

So, 2d1=26 ⇒ d1=13

Hence, d1=d2=13 cm

Now, using Pythagoras theorem,

⇒ x² + y² = d²

⇒ x² + 5² = 13²

⇒ x² = 13² - 5²

⇒ x² = 169 - 25

⇒ x² = 144

⇒ x = 12

So, the length = 12 cm and the diagonals = 13 cm each.

Extra Information :

• Rectangle is a quadrilateral with opposite sides equal.
• It includes four right angles.
• The opposite sides of a rectangle are equal and parallel.
• The diagonals in a rectangle bisect each other.
• The diagonals are equal.
• The area of a rectangle is the the product of of length and breadth of the rectangle.
• The perimeter of the rectangle is 2 times the sum of length and breadth of the rectangle.
• The Pythagoras theorem states that the sum of the square of the altitude and the square of the base is equal to the square of the hypotenuse of the right angled triangle.

Answer 2

Given :-

If the sum of the diagonals of a rectangle is 26 cm and one of its side is 5 cm,

To Find :-

Length of side and diagnal

Solution :-

We know that

Diagonal 1 = Diagonal 2

Let the diagonal be d

So,

d + d = 26

2d = 26

d = 26/2

d = 13

Length of diagonal = 13 cm

Now

Diagonal² = Length² + Breadth²

(13)² = L² + (5)²

169 = L² + 25

169 - 25 = L²

144 = L²

√144 = L

12 = L

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