SOLUTION: find the perimeter of an isoceles right angled triangle having an area of 5000m2

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Question 1084356: find the perimeter of an isoceles right angled triangle having an area of 5000m2

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
x%2Bx%2Bd, perimeter
d, diagonal hypotenuse
x, each leg

x is also height and a base.
%281%2F2%29x%2Ax=5000
x%5E2=10000
highlight_green%28x=100%29

Isosceles RIGHT Triangle.
x%5E2%2Bx%5E2=d%5E2, Pythagorean Theorem Formula
2x%5E2=d%5E2
d=x%2Asqrt%282%29
highlight_green%28d=100%2Asqrt%282%29%29

Perimeter: 100%2B100%2B100%2Asqrt%282%29
highlight%28200%2B100%2Asqrt%282%29%29

Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the length of either leg (the legs are congruent, since the triangle is isosceles).


Then the area of this right-angled triangle is %281%2F2%29%2Ax%2Ax = 5000 m^2, which implies

x%5E2 = 10000 m^2, i.e.   x = 100 m.


Then the hypotenuse is 100%2Asqrt%282%29 and the perimeter is 200%2B+100%2Asqrt%282%29 m.

Solved.


Notice that "josgarithmetic" mistakenly uses the term "diagonal", which is not applicable in this case.