A right-angled triangle has a hypotenuse of length 2 + √2?
and one other side of length 1 + √2. Find exact values for the length of the third side and the area.
I got 3 + 2√2 for the 3rd side, but the answers in my textbook has other ideas. What do you think?
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Let length = l
l^2 + (1+ √2)^2 = (2 + √2)^2
l^2 + 1 + 2√2 + 2 = 4 + 4√2 + 2
l^2 = 6 - 3 + 4√2 - 2√2
l^2 = 3 + 2√2
l^2 = 4.14
l = 2.1 units
Hello,
It bears repeating: you should have applied the well-known following formulas: "Hello", "Please" and "Thanks".
Anyway...
= = = = = = = = = = = = = = = = = =
Using Pythagora's theorem:
(Hypothenuse)² = (one side of the right angle)² + (other side)²
(2 + √2)² = (1 + √2)² + (other side)²
(other side)² = (2 + √2)² – (1 + √2)²
(other side)² = (4 + 4√2 + 2) – (1 + 2√2 + 2)
(other side)² = (6 + 4√2) – (3 + 2√2)
(other side)² = 3 + 4√2
(other side)² = (1 + 4√2 + 2)
(other side)² = (1 + √2)²
other side = 1 + √2
Thus the 3rd side is worth 1+√2 and equals the 2nd side
making the right triangle also isosceles.
Its area will then be
(1 + √2)²/2 = (3 + 4√2)/2 = (3/2) + 2√2
Regards,
Dragon.Jade :-)