The sides of a right-angled triangle containing the right angle are 5x cm and (3x – 1) cm. Calculate the length of the hypotenuse of the triangle if its area is 60 cm².
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The sides of a right-angled triangle containing the right angle are 5x cm and (3x – 1) cm. Calculate the length of the hypotenuse of the triangle if its area is 60 cm².

KnowledgeBoat · Accepted Answer

Consider △ABC as a right angled triangle. AB = 5x cm and BC = (3x – 1) cm We know that, Area of △ABC = × base × height = × BC × AB Substituting the values we get, ⇒ 60 = × (3x – 1) × 5x ⇒ 120 = 5x(3x – 1) ⇒ 120 = 15x² – 5x ⇒ 15x² – 5x – 120 = 0 ⇒ 5(3x² – x – 24) = 0 ⇒ 3x² – x – 24 = 0 ⇒ 3x² – 9x + 8x – 24 = 0 ⇒ 3x(x – 3) + 8(x - 3) = 0 ⇒ (3x + 8)(x - 3) = 0 ⇒ 3x + 8 = 0 or x - 3 = 0 ⇒ 3x = -8 or x = 3 ⇒ x = or x = 3 Since, x cannot be negative as length of a side cannot be negative. So, x = 3. AB = 5 × 3 = 15 cm BC = (3 × 3 – 1) = 9 – 1 = 8 cm In right angled △ABC, Using Pythagoras theorem, ⇒ AC² = AB² + BC² Substituting the values we get, ⇒ AC² = 15² + 8² ⇒ AC² = 225 + 64 = 289 ⇒ AC² = 17² So, AC = 17 cm. Hence, the hypotenuse of the right angled triangle is 17 cm.

Mathematics

The sides of a right-angled triangle containing the right angle are 5x cm and (3x – 1) cm. Calculate the length of the hypotenuse of the triangle if its area is 60 cm².

Mensuration

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Mathematics

The sides of a right-angled triangle containing the right angle are 5x cm and (3x – 1) cm. Calculate the length of the hypotenuse of the triangle if its area is 60 cm2.

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