The lengths of the sides of a right triangle are (2x − 1) m, (4x) m and (4x + 1) m, where x > 0. Find :
(i) the value of x,
(ii) the area of the triangle.

Question

The lengths of the sides of a right triangle are (2x − 1) m, (4x) m and (4x + 1) m, where x 0. Find : (i) the value of x, (ii) the area of the triangle.

KnowledgeBoat · Accepted Answer

(i) Given, Length of three sides of right angled triangle are (2x - 1) m, (4x) m, (4x + 1) m. The largest side is hypotenuse = (4x + 1) m By pythagoras theorem, ⇒ (2x - 1)2 + (4x)2 = (4x + 1)2 ⇒ 4x2 - 4x + 1 + 16x2 = 16x2 + 8x + 1 ⇒ 4x2 - 4x + 1 + 16x2 - 16x2 - 8x - 1 = 0 ⇒ 4x2 - 12x = 0 ⇒ 4x(x - 3) = 0 ⇒ 4x = 0 or x - 3 = 0 ⇒ x = 0 or x = 3 Since, x 0. x = 3. Hence, value of x = 3. (ii) Calculating the sides of triangle, Length of first side = 2x - 1 = 2(3) - 1 = 6 - 1 = 5 m Length of second side = 4x = 4(3) = 12 m Length of hypotenuse = 4x + 1 = 4(3) + 1 = 13 m By formula, Area of triangle = base × height = × 5 × 12 = 30 m2. Hence, area of triangle = 30 m2.

Mathematics

The lengths of the sides of a right triangle are (2x − 1) m, (4x) m and (4x + 1) m, where x > 0. Find :
(i) the value of x,
(ii) the area of the triangle.

Quadratic Equations

Related Questions

The hypotenuse of a right triangle is 20 m. If the difference between the lengths of other sides be 4 m, find the other sides.

Two squares have sides x cm and (x + 5) cm. The sum of their areas is 697 sq. cm.
(i) Express this as an algebraic equation in x.
(ii) Solve this equation to find the sides of the squares.

The area of a right-angled triangle is 96 m². If its base is three times its altitude, find the base.

Mathematics

The lengths of the sides of a right triangle are (2x − 1) m, (4x) m and (4x + 1) m, where x > 0. Find :(i) the value of x,(ii) the area of the triangle.

Quadratic Equations

Related Questions

The hypotenuse of a right triangle is 20 m. If the difference between the lengths of other sides be 4 m, find the other sides.

Two squares have sides x cm and (x + 5) cm. The sum of their areas is 697 sq. cm.(i) Express this as an algebraic equation in x.(ii) Solve this equation to find the sides of the squares.

The area of a right-angled triangle is 96 m2. If its base is three times its altitude, find the base.

The lengths of the sides of a right triangle are (2x − 1) m, (4x) m and (4x + 1) m, where x > 0. Find :
(i) the value of x,
(ii) the area of the triangle.

Two squares have sides x cm and (x + 5) cm. The sum of their areas is 697 sq. cm.
(i) Express this as an algebraic equation in x.
(ii) Solve this equation to find the sides of the squares.

The area of a right-angled triangle is 96 m². If its base is three times its altitude, find the base.