SOLUTION: If we have a 90° triangle and one of the sides is 20x and the other is 9x find the hypotenus.The area is 720 cm^(2)

Algebra ->  Triangles -> SOLUTION: If we have a 90° triangle and one of the sides is 20x and the other is 9x find the hypotenus.The area is 720 cm^(2)      Log On


   

Question 936034: If we have a 90° triangle and one of the sides is 20x and the other is 9x find the hypotenus.The area is 720 cm^(2)
Found 2 solutions by srinivas.g, MathLover1:
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
one side = 20 x
other side = 9x
area = 720 cm^2
area = +%281%2F2%29%2A+one+side+%2Aother+side
720 = +%281%2F2%29%2A20x%2A9x
720+=+10x%2A9x
720+=+90+x%5E2
divide with 90 on both sides
+720%2F90+=++90+x%5E2+%2F90
+8+=+x%5E2
as per Pythagorean theorem
+hypotenuse+%5E2+=++base+%5E2%2B+height+%5E2
so hypotenuse+%5E2+=++oneside+%5E2%2B+otherside%5E2
+hypotenuse%5E2++=+%2820x%29%5E2%2B%289x%29%5E2
++hypotenuse%5E2++=+400+x%5E2%2B81+x%5E2
+hypotenuse%5E2+=481+x%5E2
but+x%5E2+=8
+hypotenuse%5E2+=481+x%5E2
+hypotenuse+%5E2++=+481%2A8
+hypotenuse%5E2+=3848
+hypotenuse++=+sqrt%283848%29
hypotenuse = 62.03 cm
Result : Hypotenuse = 62.03 cm

Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

If we have a 90° triangle and one of the sides is a=20x and the other is b=9x find the hypotenuse.
The area is
720cm%5E2=%281%2F2%29a%2Ab
720cm%5E2=%281%2F2%2920x%2A9x
720cm%5E2=10x%2A9x
720cm%5E2=90x%5E2
720cm%5E2%2F90=x%5E2
72cm%5E2%2F9=x%5E2
8cm%5E2=x%5E2
x=sqrt%288cm%5E2%29
x=2.82842712474619cm

the hypotenuse c%5E2=a%5E2%2Bb%5E2
c%5E2=%2820x%29%5E2%2B%289x%29%5E2
c=sqrt%28400x%5E2%2B81x%5E2%29
c=sqrt%28481x%5E2%29
c=21.93171219946131x
c=21.93171219946131%2A2.82842712474619cm
c=62.03224967708329cm

a=20%2A2.82842712474619cm
a=56.5685424949238cm
b=9%2A2.82842712474619cm
b=25.45584412271571cm

check:
c%5E2=a%5E2%2Bb%5E2
%2862.03224967708329cm%29%5E2=%2856.5685424949238cm%29%5E2%2B%2825.45584412271571cm%29%5E2
3848cm%5E2=3200cm%5E2%2B648cm%5E2
3848cm%5E2=3848cm%5E2

720cm%5E2=%281%2F2%29a%2Ab
720cm%5E2=%281%2F2%2956.5685424949238cm%2A25.45584412271571cm
720cm%5E2=%281%2F2%291440cm%5E2
720cm%5E2=720cm%5E2
ps: only if you use all decimal places you can get exact result