Question

The diagonals of a rhombus measure 10 cm and 24 cm respectively. What is its area? What is the measure
of each side?

Answer 1

★$\huge\bf{\blue{\underline{Question:-}}}$

The diagonals of a rhombus measure 10 cm and 24 cm respectively. What is its area? What is the measure

of each side?

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★$\huge\bf{\red{\underline{Answer:-}}}$

52cm.

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★$\huge\bf{\green{\underline{Explanation:-}}}$

➡Diagonals of the rhombus = 10cm, 24cm

➡Since the diagonals meet at the centre of the rhombus, they create 4 right angles in the centre.

➡So, in this case, we can use the Pythagoras theorem, which states that the sum of the squares on the height and base of a right angle is equal to the square on the hypotenuse.

So, moving on to your solution...

➡Length of the base = 10/2 = 5cm

➡Length of the height = 24/2 = 12cm

By Pythagoras theorem,

➡Hypotenuse = 5^2 + 12^2

➡Hypotenuse = 25 + 144

➡Hypotenuse = 169^2

➡Hypotenuse = 13cm

So, the side of the rhombus is 13cm.

➡Perimeter of the rhombus = 4×side

➡= 4 × 13

➡= 52cm.

Therefore, the perimeter of the rhombus is 52cm.

Hope helped!!

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Answer 2

➡Diagonals of the rhombus = 10cm, 24cm

➡Since the diagonals meet at the centre of the rhombus, they create 4 right angles in the centre.

➡So, in this case, we can use the Pythagoras theorem, which states that the sum of the squares on the height and base of a right angle is equal to the square on the hypotenuse.

So, moving on to your solution...

➡Length of the base = 10/2 = 5cm

➡Length of the height = 24/2 = 12cm

By Pythagoras theorem,

➡Hypotenuse = 5^2 + 12^2

➡Hypotenuse = 25 + 144

➡Hypotenuse = 169^2

➡Hypotenuse = 13cm

So, the side of the the rhombus is 13cm.

➡Perimeter of the rhombus = 4×side

➡= 4 × 13

➡= 52cm.

Therefore, the perimeter of the rhombus is 52cm.