Question

The legs of right triangle are in the ratio 3:4 and its area is 1014 cm2. Find its hypotenuse

Answer 1

Answer:

the answer of your question is 65

Step-by-step explanation:

Answer 2

Given :-

• The legs of right triangle are in the ratio 3:4 and its area is 1014 cm².

To Find :-

• Hypotenuse.

Solution :-

❏ As we know that Area of Triangle is given by [ Area of Triangle = ½ × Base × Height ] and in this question we also use Pythagoras theorem I.e (H)² = (P)² + (B)² where H, P and B stands for Hypothenuse , Perpendicular and Base respectively.

➟ Let the Base of the Triangle be 3x

➟ Let the Height of the Triangle be 4x

According to the Situation :

➝ Area of Triangle = ½ × Base × Height

➝ ⠀⠀⠀⠀⠀⠀⠀1014 = ½ × 3x × 4x

➝ ⠀⠀⠀⠀⠀⠀⠀1014 = 3x × 2x

➝ ⠀⠀⠀⠀⠀⠀⠀1014 = 6x²

➝ ⠀⠀⠀⠀⠀⠀⠀1014 / 6 = x²

➝ ⠀⠀⠀⠀⠀⠀⠀169 = x²

➝ ⠀⠀⠀⠀⠀⠀⠀√169 = x

➝ ⠀⠀⠀⠀⠀⠀⠀⠀13 = x

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Therefore :

• Perpendicular of Triangle = 3x = 3 × 13 = 39
• Base of Triangle = 4x = 4 × 13 = 52

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Applying Pythagoras theorem :

➞ (H)² = (P)² + (B)²

➞ (H)² = (39)² + (52)²

➞ (H)² = 1521 + 2704

➞ (H)² = 4225

➞ H = √4225

➞ H = 65cm

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Verification :-

⟾ (H)² = (P)² + (B)²

⟾ (65)² = (39)² + (52)²

⟾ 4225 = 1521 + 2704

⟾ 4225 = 4225

Hence Verified

Thus, Hypothenuse of the Triangle = 65cm

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