If the lengths of the sides of a triangle are in the ratio 3: 4 : 5 and its perimeter is 48 cm, find its area.

Let a, b and c be the sides of the triangle. Given, Ratio of the sides are 3 : 4 : 5. Let a = 3x cm, b = 4x cm and c = 5x cm. Given, ⇒ Perimeter = 48 cm ⇒ a + b + c = 48 ⇒ 3x + 4x + 5x = 48 ⇒ 12x = 48 ⇒ x = = 4. Substituting value of x, a = 3x = 3 × 4 = 12 cm, b = 4x = 4 × 4 = 16 cm, c = 5x = 5 × 4 = 20 cm. We know that, Semi perimeter (s) = . Area of triangle = Substituting values we get, Hence, area of triangle = 96 cm 2 .

If the perimeter of an equilateral triangle is 36 cm, calculate its area and height.

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ABC is a triangle in which AB = AC = 4 cm and ∠A = 90°. Calculate the area of △ABC. Also find the length of perpendicular from A to BC.

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Mathematics

If the lengths of the sides of a triangle are in the ratio 3: 4 : 5 and its perimeter is 48 cm, find its area.

Mensuration

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If the perimeter of an equilateral triangle is 36 cm, calculate its area and height.

ABC is a triangle in which AB = AC = 4 cm and ∠A = 90°. Calculate the area of △ABC. Also find the length of perpendicular from A to BC.