Question

The hypotenuse of a right angled triangle is 17cm and the difference between other two sides is 7cm. Find the sides and its Perimeter.​

Answer 1

Required Answer :

• First side = 10 cm
• Second side = 17 cm
• Perimeter of the triangle = 44 cm

Given :

• Hypotenuse of a right angled triangle = 17 cm
• The difference between the other two sides = 7

To find :

• The two sides
• The perimeter of triangle

Solution :

Let,

• The first side of triangle = x cm
• The second side of triangle = x + 7 cm

Using pythagoras theorem,

• H² = P² + B²

where,

• H denotes the hypotenuse
• P denotes the perpendicular
• B denotes the base

⇒ (17)² = (x)² + (x + 7)²

⇒ 289 = x² + x² + 49 + 14x

⇒ 289 = 2x² + 49 + 14x

⇒ 2x² + 49 + 14x - 289 = 0

⇒ 2x² + 14x - 240 = 0

⇒ 2(x² + 2x - 120) = 0

⇒ x² + 2x - 120 = 0

⇒ x² + 12x - 10x - 120 = 0

⇒ x(x + 12) - 10(x + 12) = 0

⇒ (x - 10)(x + 12) = 0

⇒ (x - 10) = 0 or (x + 12) = 0

⇒ x = 10 or x = - 12 Reject - ve

Therefore,

• The value of x = 10

The other two sides of triangle :

First side :

⇒ First side = x

⇒ First side = 10 cm

Second side :

⇒ Second side = x + 7

⇒ Second side = 10 + 7

⇒ Second side = 17 cm

Using formula,

• Perimeter of triangle = sum of all sides

⇒ Perimeter = 17 + 10 + 17

⇒ Perimeter = 44

Therefore,

• Perimeter of the triangle = 44 cm