If the area of a triangle is 54cm^2 form a quadratic equation

Question

to find x which has a 15cm long hypotenuse and the base is x?

 

Answer 1

Length of hypotenuse = 15 cm.

base = x.

Let the height be h.

By pythagoras theorem, 15² = x² + h²

h² = 15² - x²

h = √(15² - x²)

= √(225 - x²)

Area of triangle A = 1/2 base * height.

54 = 1/2 * x * √(225 - x²)

54 = x √(225 - x²) / 2

Squring on both sides we get,

54² =[ x √(225 - x²) / 2 ]²

2916 = x²(225 - x²)/4

2916 = (225x² - x⁴)/4

Multiply each side by 4.

2916 * 4 = (225x² - x⁴)/4 * 4

11664 = 225x² - x⁴

x⁴- 225x² +  11664 = 0

x⁴- 225x² +  11664 = 0

Take positive term.

Take negative term.

Therefore base of the triangle is 9 cm or 12cm.