Question

the sides of a right angled trianglr containing the right angle are 3(x+1)cm and (2x-1)cm .If area of triangle is 30sq.cm. Find the lengths of the sides of the triangle.​

Answer 1

Answer:

The length of the sides of the triangle are 12 cm, 5 cm and 13 cm respectively.

Step-by-step explanation:

Given:

• The sides of a right angled triangle containing the right angle are 3(x+1)cm and (2x-1)cm.
• Area of triangle is 30 cm².

To find:

• The lengths of the sides of the triangle.

Solution:

♦ Area of a rectangle = 1/2 × b × h

Where,

b is the base of a triangle.

h is the height of a triangle.

Putting the values in the formula, we have:

• 30 = 1/2 × 3(x + 1) × (2x - 1)
• 30 = 1/2 × (3x + 3) × (2x - 1)
• 30 = 1/2 × 3x(2x - 1) +3(2x - 1)
• 30 = 1/2 × 6x² - 3x + 6x - 3
• 30 × 2 = 6x² - 3x + 6x - 3
• 60 = 6x² + 3x - 3
• 6x² + 3x - 3 - 60 = 0
• 6x² + 3x - 63 = 0

Use quadratic formula,

♦ x = (- b ± √b² - 4ac )/2a

Here,

a = 6

b = 3

c = 63

Putting the values,

Refer the attachment!!

We will take positive value of x because the sides of triangle can't be negative.

• x = 3

Now, finding the sides.

• AB = 3(3+1)cm
• AB = 3 × 4 cm
• AB = 12 cm

• BC = (2 × 3 -1)cm
• BC = (6 - 1 ) cm
• BC = 5 cm

• AC = √(12² + 5²) cm
• AC = √(144 + 25) cm
• AC = √169 cm
• AC = 13 cm

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