please solve this problem in explanation
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Answer:
Step-by-step explanation:
diagnols of rhombhus=10cm 24cm
perimeter=2(sum of diagnols)
=2(10+24)
=2(34)
=68
Answered by
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Question:
The diagonals of a rhombus measure 10cm and 24cm. Find its perimeter.
Solution:
Let diagonals of the rhombus be d₁ = 10cm and d₂ = 24cm.
By using Pythagoras theorem,
- Length of the base = 10/2 = 5cm.
- Length of the height = 24/2 = 12cm.
Finding the other side of rhombus.
(Hypotenuse)² = (side)² + (side)²
⟹ Hypotenuse² = (5)² + (12)²
⟹ Hypotenuse² = 25 + 144
⟹ Hypotenuse² = 169
⟹ Hypotenuse = √169
⟹ 13cm
∴ The side of the rhombus is 13cm.
Now,
Perimeter of the rhombus = ?
Perimeter of the rhombus = 4 × side.
⟹ 4 × side
⟹ 4 × 13
⟹ 52cm
∴ The perimeter of the rhombus is 52cm.
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