Question

The hypotenuse of a right angled triangle is 2√13cm.If the smaller side is increased by 2 cm and the larger side is increased by 3cm, the new hypotenuse will be √117cm . Find the length of the larger side of the right angled triangle. ​

Answer 1

Answer:

Step-by-step explanation:

Length of the longer side = 6cm

Answer 2

Let :-

• The length of smaller side = X
• The length of larger side = Y

To Find :-

• The length of larger side = ?

Solution :-

• To calculate the length of larger side of right angle triangle at first we have to set up equation by using clue in the given Question. The. solve the equation.

Calculation for 1st equation :-

⇢By using Pythagoras theorem :-

⇢Small side² + large side² = Hypotenuse ²

⇢ x² + y² = (2√13)²-------(i)

Calculation for 2nd equation :-

⇢ By using Pythagoras theorem :-

Small side = (x + 2). Large side = (y + 3) :-

⇢ (x + 2)² + (y + 3)² = (√117)²

⇢ x² + 4x + 4 + y² + 6y + 9 = 117

⇢ x² + y² + 4x + 6y + 13 = 117

⇢ x² + y² + 4x + 6y = 117 - 13

⇢ x² + y² + 4x + 6y = 104

• Putting x² + y² = (2√13)² from eq (i) :-

⇢ (2√13)² + 4x + 6y = 104

⇢ 52 + 4x + 6y = 104

⇢ 4x + 6y = 104 - 52

⇢ 4x + 6y = 52

⇢ 4x = 52 - 6y

⇢ x = (52 - 6y)/4------(ii)

• Putting the value of x in eq (i) :-]

⇢ x² + y² = (2√13)²

⇢{(52 - 6y)/4}² + y² = 52

⇢ (2704 - 624y + 36y²)/16 + y² = 52

⇢ (2704 - 624y + 36y² + 16y²)/16 = 52

⇢ 52y² - 624y + 2704 = 52 × 16

⇢ 52y² - 624y + 2704 - 832 = 0

⇢ 52y² - 624y + 1872 = 0

• Dividing by 52 on both sides :-]

⇢ y² - 12y + 36 = 0

• Splitting middle term here :-]

⇢ y² - 6y - 6y + 36 = 0

⇢ y(y - 6) - 6(y - 6) = 0

⇢ (y - 6)(y - 6) = 0

⇢ y - 6 = 0 ⇢ y = 6

Hence, The larger side of the ∆ (y) = 6cm :-