If the hypotenuse of a triangle is 12 cm and the measure of its legs are in the ratio 1:2, then what are the measures of it’s legs?

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bedevijuo3e · Accepted Answer

Step 1Here is a way to solve without directly using Pythagoras theorem.Let a, b and c be the side lengths of the given right triangle such that c is is the length of hypotenuse.Measure of legs are in the ratio 1:2Let a=x, b=2xLet R and r be the circumradius and inradius of right triangle respectively.R=c2=122=6r=aba+b+c=x×2xx+2x+12=2x23x+12We have,R+r=a+b26+2x23x+12=x+2x2(3x+12)(3x−12)=4x25x2−144=0⇒x=125a=125b=2×125=245

junoon363km · Accepted Answer

Step 1If the triangle has a hypotenuse, I’ll assume that the triangle is right angled.Mr. Pythagoras says that the hypotenuse squared = leg 1 squared plus leg 2 squared.leg 1=1xleg 2=2xleg 12+leg 22=hypotenuse2(1x)2+(2x)2=122(1x2})+(4x2)=1445x2=122x2=1445x2=28.8x=5.367 cm2x=2×5.367=10.733 cmStep 2Proof:If both sides of this equation are equal, then the answer is right.122=≠5.3672+10.7332144=≠28.8+115.2144=144One leg of the triangle is 5.367 cm and the second leg is 10.733 cm.

If the hypotenuse of a triangle is 12 cm and

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