In △ABC, ∠B = 90°, AB = (2x + 1) cm and BC = (x + 1) cm. If the area of the △ABC is 60 cm 2 , find its perimeter.

Given, AB = (2x + 1) cm BC = (x + 1) cm We know that, Area of △ABC = × base × height = × BC × AB Substituting the values we get, ⇒ 60 = × (x + 1) × (2x + 1) ⇒ 60 × 2 = (2x + 1)(x + 1) ⇒ 120 = 2x 2 + 3x + 1 ⇒ 2x 2 + 3x + 1 – 120 = 0 ⇒ 2x 2 + 3x – 119 = 0 ⇒ 2x 2 + 17x – 14x – 119 = 0 ⇒ x(2x + 17) – 7(2x + 17) = 0 ⇒ (x – 7)(2x + 17) = 0 ⇒ x – 7 = 0 or 2x + 17 = 0 ⇒ x = 7 or 2x = -17 ⇒ x = 7 or x = Since, x cannot be negative as length of a side cannot be negative. So, x = 7. ⇒ AB = (2x + 1) = 2 × 7 + 1 = 15 cm ⇒ BC = (x + 1) = 7 + 1 = 8 cm. In right angled △ABC, Using Pythagoras Theorem, ⇒ AC 2 = AB 2 + BC 2 Substituting the values we get, ⇒ AC 2 = 15 2 + 8 2 ⇒ AC 2 = 225 + 64 ⇒ AC 2 = 289 ⇒ AC 2 = 17 2 ⇒ AC = 17 cm Perimeter of △ABC = AB + BC + AC = 15 + 8 + 17 = 40 cm. Hence, perimeter of △ABC = 40 cm.

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Mathematics

In △ABC, ∠B = 90°, AB = (2x + 1) cm and BC = (x + 1) cm. If the area of the △ABC is 60 cm², find its perimeter.

Mensuration

Related Questions

The sides of a right-angled triangle containing the right angle are 5x cm and (3x – 1) cm. Calculate the length of the hypotenuse of the triangle if its area is 60 cm².

The perimeter of an isosceles triangle is 40 cm. The base is two third of the sum of equal sides. Find the length of each side.

If the perimeter of a right angled triangle is 60 cm and its hypotenuse is 25 cm, find its area.

Find the area of an isosceles triangle whose base is 6 cm and perimeter is 16 cm.

Mathematics

In △ABC, ∠B = 90°, AB = (2x + 1) cm and BC = (x + 1) cm. If the area of the △ABC is 60 cm2, find its perimeter.

Mensuration

Related Questions

The sides of a right-angled triangle containing the right angle are 5x cm and (3x – 1) cm. Calculate the length of the hypotenuse of the triangle if its area is 60 cm2.

The perimeter of an isosceles triangle is 40 cm. The base is two third of the sum of equal sides. Find the length of each side.

If the perimeter of a right angled triangle is 60 cm and its hypotenuse is 25 cm, find its area.

Find the area of an isosceles triangle whose base is 6 cm and perimeter is 16 cm.

In △ABC, ∠B = 90°, AB = (2x + 1) cm and BC = (x + 1) cm. If the area of the △ABC is 60 cm², find its perimeter.

The sides of a right-angled triangle containing the right angle are 5x cm and (3x – 1) cm. Calculate the length of the hypotenuse of the triangle if its area is 60 cm².