SOLUTION: In a right triangle, the ratio of the legs is one to two. If the area of the triangle is twenty-five square centimeters, what is the length of the longest leg?

Algebra ->  Triangles -> SOLUTION: In a right triangle, the ratio of the legs is one to two. If the area of the triangle is twenty-five square centimeters, what is the length of the longest leg?       Log On


   

Question 690846: In a right triangle, the ratio of the legs is one to two. If the area of the triangle is twenty-five square centimeters, what is the length of the longest leg?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The area of the right triangle is
+A+=+%281%2F2%29%2Ab%2Ah+
where +b+ is the base and +h+
is the height
given: +h+=+2b+
By substitution:
+A+=+%281%2F2%29%2Ab%2A2b+
+A+=+b%5E2+
given: +A+=+25+ cm2
+25+=+b%5E2+
+b+=+5+
The longest leg is +2b+, so
+2b+=+10+
The longest leg is 10 cm
check:
+A+=+%281%2F2%29%2Ab%2Ah+
+A+=+%281%2F2%29%2A5%2A10+
+A+=+50%2F2+
+A+=+25+
OK