If the difference between the sides of a right angled triangle is 3 cm and its area is 54 cm 2 ; find its perimeter.

Given: Area = 54 cm 2 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 = x 2 - 3x ⇒ x 2 - 3x - 108 = 0 ⇒ x 2 - 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, AB 2 + BC 2 = AC 2 ⇒ 12 2 + 9 2 = AC 2 ⇒ 144 + 81 = AC 2 ⇒ 225 = AC 2 ⇒ 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.

Calculate the area and the height of an equilateral triangle whose perimeter is 60 cm.

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In triangle ABC; angle A = 90°, side AB = x cm, AC = (x + 5) cm and area = 150 cm². Find the sides of the triangle.

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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.

Mensuration

Related Questions

Calculate the area and the height of an equilateral triangle whose perimeter is 60 cm.

In triangle ABC; angle A = 90°, side AB = x cm, AC = (x + 5) cm and area = 150 cm². Find the sides of the triangle.

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

Related Questions

Calculate the area and the height of an equilateral triangle whose perimeter is 60 cm.

In triangle ABC; angle A = 90°, side AB = x cm, AC = (x + 5) cm and area = 150 cm2. Find the sides of the triangle.

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

In triangle ABC; angle A = 90°, side AB = x cm, AC = (x + 5) cm and area = 150 cm². Find the sides of the triangle.