ABC is a right angled triangle. All the measurements are in cm. AB = x
BC = (x+2)
AC = (x+4)
Use the information to form a quadratic equation of the form x^2 + ax + b = 0, where a and b are constants which you need to find.

Step-by-step explanation:

By Pythagoras' Theorem,

we have x² + (x + 2)² = (x + 4)².

=> 2x² + 4x + 4 = x² + 8x + 16

=> x² - 4x - 12 = 0

(The constants are a = -4, b = -12)

=> (x - 6)(x + 2) = 0

=> x = 6 or x = -2

The value x = -2 is rejected as side lengths cannot be negative.

Hence we have x = 6.

=> AB = 6cm, BC = 8cm, AC = 10cm.

P.S. What you see above is the full solution. You just need to type x² - 4x - 12 = 0 in the blank.

step-by-step explanation:

the areas of two similar triangles are 18 cm2 and 8 cm2. one of the sides of the first triangle is 4.5 cm. what is the length of the corresponding side of the other triangle?