SOLUTION: Hi. My name is Allen and I'm not able to figure out how to do this problem. Your response is appreciated. (a) A right-angled triangle has a 45 degree angle. If the area is 2 cm

Question 702586: Hi. My name is Allen and I'm not able to figure out how to do this problem. Your response is appreciated.
(a) A right-angled triangle has a 45 degree angle. If the area is 2 cm^2 what is the length of the perimeter?
(b) Same question, but this time the area is A cm^2
(a) perimeter= _________ cm
(b) perimeter= _________ cm
Thank You!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
(a) A right-angled triangle has a 45 degree angle. If the area is 2 cm^2 what is the length of the perimeter?
Sketch a right triangle with two 45 degree angles.
The base and the height are equal; let each be "x".
-----
Area = (1/2)(base)*(height) = (1/2)x^2
-------------------------------
Equation:
(1/2)x^2 = 2 cm^2
x^2 = 4 cm^2
x = 2 cm
------
Hypotenuse^2 = x^2 + x^2
h^2 = 2^2 + 2^2
h^2 = 8
h = 2sqrt(2) cm
Perimeter = 2 + 2 + 2sqrt(2) = (4 + 2sqrt(2)) cm
-----------------------------------------
(b) Same question, but this time the area is A cm^2
(1/2)x^2 = A cm^2
x^2 = 2A
x = sqrt(2A)
------------
hypotenuse^2 = (2A) + (2A)
h = 2sqrt(A)
Perimeter = 2sqrt(2A) + 4A
=====================
Cheers,
Stan H.
====================
(a) perimeter= _________ cm
(b) perimeter= _________ cm

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