Question

Help meeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

The length of the shorter leg is 9 mm.

The length of the longer leg is 12 mm.

The length of the hypotenuse is 15 mm.

Pythagoras theory applies to every right triangle. If

• The shorter leg = a
• The longer leg = b
• The hypotenuse = c
• 
  `a^2 + b^2 = c^2`

Explanation:

Known

• Longer leg = shorter leg +3 mm
  b = a+3 mm
• Hypotenuse = shorter leg +6 mm
  c = a+6 mm

Asked

• a?
• b?
• c?

Answer

`a^2 + b^2 = c^2`

`a^2 + (a+3)^2 = (a+6)^2`

`a^2 + a^2 + (2 * a * 3) + 3^2 = a^2 + (2 * a * 6) + 6^2`

`2a^2 + 6a + 9 = a^2 + 12a + 36`

`2a^2 - a^2 + 6a - 12a + 9 - 36 = 0`

`a^2 - 6a - 27 = 0`

`a^2 - 9a + 3a - 27 = 0`

`a * (a - 9) + 3 * (a - 9) = 0`

(a-9) (a+3)=0

a-9=0 or a+3= 0

a=9 or a=-3 (impossible)

Shorter leg

a=9 mm

Longer leg

b = a+3

b = 9+3

b = 12 mm

Hypotenuse

c = a+6

c = 9+6

c = 15 mm