Question

The difference between the sides contanig a right angle ina right angeled triangle is 14 cm the area of triangle is 120 cm square calculate the perimeter of atriangle

Answer 1

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Let's suppose, one side = x cm

Then, another side will be = (x - 14) cm.

According to the question,

Area of a triangle = ½ × base × height

=> 120 = ½ • x • (x - 14)

=> 120 = ½ • x² - 14x

=> 240 = x² - 14x

=> 0 = x² - 14x - 240

=> (x - 24)(x + 10)

∴ x = 24, -10

[Neglecting the x = -10 as it is negative. ]

∴ x = 24

Now,

Sides at the right angle are :-

• x = 24 cm.
• And, (x - 14) = 10 cm.

Calculating the third side by pythagoras theorem,

=> (third side)² = (24)² + (10)²

=> third side = 26 cm.

Hence,

Perimeter of the triangle = 24 + 10 + 26

= 60cm.