Question

the base and height of a triangle are in the ratio 3 ratio 2 and the area is 180 square cm find its base and height.​

Answer 1

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Answer 2

Correct Question :-

• The base and height of a triangle are in the ratio 3:2 and the area is 108cm² find its base and height.

Given :-

• The base and height of a triangle are in the ratio 3:2
• The Area of the Triangle is 108cm²

To Find :-

• Base and Height of the Triangle.

Solution :-

❏ As we know that, Area of Triangle is given by [ Area of Triangle = ½ × Base × Height ]

⟼ Let the Base of Triangle be 3x

⟼ Let the Height of Triangle be 2x

Putting the Values :

➞ Area of Triangle = ½ × Base × Height

➞ 108 = ½ × 3x × 2x

➞ 108 = 3x²

➞ 108 / 3 = x²

➞ 36 = x²

➞ √36 = x

➞ 6cm = x

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Verification :

⟹ Area of Triangle = ½ × Base × Height

⟹ Area of Triangle = ½ × 3x × 2x

⟹ Area of Triangle = ½ × (3 × 6) × (2 × 6)

⟹ Area of Triangle = ½ × 18 × 12

⟹ Area of Triangle = 18 × 6

⟹ 108 = 108

Hence Verified

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Therefore :

• Base of Triangle = 3x = 3 × 6 = 18cm
• Height of Triangle = 2x = 2 × 6 = 12cm

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