Question

The legs of a right triangle are 4cm and x cm. The hypotenuse is (2x-1)cm. What is x?

Answer 1

x = 3

Explanation:

Using Pythagoras' theorem on the right triangle, then

(2x - 1)² = 4² + x² ← expand parenthesis on the left side and simplify

4x² - 4x + 1 = 16 + x² ( subtract 16 + x² from both sides )

3x² - 4x - 15 = 0 ← in standard form

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 3 × - 15 = - 45 and sum = - 4

The factors are - 9 and + 5

Use these factors to split the x- term

3x² - 9x + 5x - 15 = 0 ( factor the first/second and third/fourth terms )

3x(x - 3) + 5(x - 3) ← factor out (x - 3)

(x - 3)(3x + 5) = 0

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

3x + 5 = 0 ⇒ 3x = - 5 ⇒ x = -
`(5)/(3)`

However, x must be greater than zero

Hence x = 3 cm

Answer 2

Explanation:

(2x-1)²=x²+4²

4x²-4x+1=x²+16

3x²-4x-15=0

a=3 b=-4 c= -15

D=b²-4ac

=16-4*3*(-15)=196

x1=-b+√D/2a=4+14/6=3

x2=-b-√D/2a=4-14/6=-10/6=-5/3