If the difference between the sides of a right angled triangle is 3 cm and its area is 54 cm²; find its perimeter.
Mensuration
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If the difference between the sides of a right angled triangle is 3 cm and its area is 54 cm²; find its perimeter.

KnowledgeBoat · Accepted Answer

Given: Area = 54 cm² Let the two sides of the right-angled triangle be x cm and (x - 3) cm. Area = x base x height ⇒ 54 = x BC x AB ⇒ 54 = (x - 3) x ⇒ 54 2 = (x - 3) x ⇒ 108 = x² - 3x ⇒ x² - 3x - 108 = 0 ⇒ x² - 12x + 9x - 108 = 0 ⇒ x(x - 12) + 9(x - 12) = 0 ⇒ (x - 12)(x + 9) = 0 ⇒ x = 12 or -9 Since length cannot be negative, AB is 12 cm. BC = (x - 3) cm = 12 - 3 cm = 9 cm By using the Pythagoras theorem, AB² + BC² = AC² ⇒ 12² + 9² = AC² ⇒ 144 + 81 = AC² ⇒ 225 = AC² ⇒ AC = ⇒ AC = 15 Perimeter of right angled triangle = AB + BC + AC = 12 + 9 + 15 cm = 36 cm Hence, the perimeter of the triangle is 36 cm.

Mathematics

If the difference between the sides of a right angled triangle is 3 cm and its area is 54 cm²; find its perimeter.

Mensuration

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Mathematics

If the difference between the sides of a right angled triangle is 3 cm and its area is 54 cm2; find its perimeter.

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