The sides of a right-angled triangle containing the right angle are (5x) cm and (3x - 1) cm. If its area is 60 cm², find its perimeter.
Mensuration
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Question

The sides of a right-angled triangle containing the right angle are (5x) cm and (3x - 1) cm. If its area is 60 cm2, find its perimeter.

KnowledgeBoat · Accepted Answer

Let ABC be a right-angled triangle, AB = 5x cm and BC = (3x – 1) cm We know that, Area of △ ABC = × base × height 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. 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 ⇒ AC2 = 289 ⇒ AC = ⇒ AC = 17 cm. Perimeter of a triangle = Sum of all the sides of a triangle = AB + BC + AC = 15 + 8 + 17 = 40 cm. Hence, perimeter of the triangle = 40 cm.

Mathematics

The sides of a right-angled triangle containing the right angle are (5x) cm and (3x - 1) cm. If its area is 60 cm², find its perimeter.

Mensuration

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