The sides of a right triangle containing the right angle are 5x cm, (3x - 1) cm. If the area of the triangle be , calculate the length of the sides of the triangle.

Question

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, Hypotenuse2 = Perpendicular2 + Base2 ⇒ AC2 = AB2 + BC2 Substituting the values we get, ⇒ AC2 = 152 + 82 ⇒ AC2 = 225 + 64 ⇒ AC2 = 289 ⇒ AC = ⇒ AC = 17 cm. Hence, the length of the sides of the triangle is 17 cm, 15 cm and 8 cm.

Mathematics

The sides of a right triangle containing the right angle are 5x cm, (3x - 1) cm. If the area of the triangle be , calculate the length of the sides of the triangle.

Pythagoras Theorem

Related Questions

In a rhombus PQRS, side PQ = 17 cm and diagonal PR = 16 cm. Calculate the area of the rhombus.

From the given figure, find the area of trapezium ABCD.

In a rhombus ABCD, prove that AC² + BD² = 4AB².

Mathematics

The sides of a right triangle containing the right angle are 5x cm, (3x - 1) cm. If the area of the triangle be , calculate the length of the sides of the triangle.

Pythagoras Theorem

Related Questions

In a rhombus PQRS, side PQ = 17 cm and diagonal PR = 16 cm. Calculate the area of the rhombus.

From the given figure, find the area of trapezium ABCD.

In a rhombus ABCD, prove that AC2 + BD2 = 4AB2.

In a rhombus ABCD, prove that AC² + BD² = 4AB².