The difference between the sides at right angles in a right-angled tri

1.	The difference between the sides at right angles in a right-angled triangle is 14 cm. The area of the triangle is 120 cm2. Calculate the perimeter of the triangle.
Answer» Suppose the sides containing right angle be x and (x – 14) cm Area of right angled triangle = \(\frac { 1 }{ 2 }\) x base x altitude = \(\frac { 1 }{ 2 }\) × x (x – 14) cm² area = 120 cm² ⇒ 120 = \(\frac { 1 }{ 2 }\) x (x² – 14x) ⇒ x² – 14x – 240 = 0 ⇒ x² – 24x + 10x – 240 = 0 ⇒ x(x – 24) + 10(x – 24) = 0 ⇒ (x – 24)(x + 10) = 0 either x – 24 = 0 ⇒ x = 24 or x + 10 = 0 ⇒ x = -10 (neglecting) x = 24 cm (one side) and another side = (x – 24) = (24 – 14) = 10 cm Hypotenuse = √(24² + 10²) = √(576 + 100) = √676 = 26 cm Perimeter of the triangle = 24 + 10 + 26 = 60 cm

The difference between the sides at right angles in a right-angled triangle is 14 cm. The area of the triangle is 120 cm2. Calculate the perimeter of the triangle.

Answer»

Suppose the sides containing right angle be x and (x – 14) cm

Area of right angled triangle

= \(\frac { 1 }{ 2 }\) x base x altitude

= \(\frac { 1 }{ 2 }\) × x (x – 14) cm²

area = 120 cm²

⇒ 120 = \(\frac { 1 }{ 2 }\) x (x² – 14x)

⇒ x² – 14x – 240 = 0

⇒ x² – 24x + 10x – 240 = 0

⇒ x(x – 24) + 10(x – 24) = 0

⇒ (x – 24)(x + 10) = 0

either x – 24 = 0

⇒ x = 24

or x + 10 = 0

⇒ x = -10 (neglecting)

x = 24 cm (one side)

and another side = (x – 24)

= (24 – 14) = 10 cm

Hypotenuse = √(24² + 10²)

= √(576 + 100)

= √676 = 26 cm

Perimeter of the triangle

= 24 + 10 + 26 = 60 cm