Question

The sides of a right triangle containing the right angle are (5x) cm and (3x-1) cm. If the area of the triangle be 60cm^2, calculate the lenght of the sides of the triangle

Answer 1

5X and 3X - 1 are the two side of the right angled triangle.

Area of triangle = 60

1/2 × 5X × ( 3X - 1 ) = 60

5X ( 3X - 1 ) = 120

15X² - 5X - 120 = 0

5 ( 3X² - X - 24 ) = 0

3X² - X - 24 = 0

3X² - 9X + 8X - 24 = 0

3X ( X - 3 ) + 8 ( X - 3 ) = 0

( X - 3 ) ( 3X + 8 ) = 0

( X - 3 ) = 0

X = 3

Hence,

its two given Sides are 15 cm and 8cm .

By Pythagoras theorem ,

Hypotenuse² = (15)² + (8)²

Hypotenuse² = 289

Hypotenuse = root 289 = 17 cm

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