SOLUTION: A triangle has sides measuring 5 cm, 5 cm and 6 cm. A second triangle is drawn with sides 5 cm, 5 cm and x cm , where x is a whole number other than 6 . If the two triangles hav

Algebra ->  Rational-functions -> SOLUTION: A triangle has sides measuring 5 cm, 5 cm and 6 cm. A second triangle is drawn with sides 5 cm, 5 cm and x cm , where x is a whole number other than 6 . If the two triangles hav      Log On


   

Question 550143: A triangle has sides measuring 5 cm, 5 cm and 6 cm. A
second triangle is drawn with sides 5 cm, 5 cm and x cm ,
where x is a whole number other than 6 . If the two triangles
have equal areas, what is the value of x?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
think of the 5-5-6 triangle with the 6 side horizontal
The area is +%281%2F2%29%2A6%2Ah%5B1%5D+%7D%7D+where+%7B%7B%7Bh%5B1%5D is the height
+h%5B1%5D+=+4+ since the height is a leg of
a 3-4-5 right triangle
---------------
The 5-5-x triangle with x side horizontal
The area is +%281%2F2%29%2Ax%2Ah%5B2%5D+
---------------
given:
+%281%2F2%29%2A6%2Ah%5B1%5D+=+%281%2F2%29%2Ax%2Ah%5B2%5D+
+6h%5B1%5D+=+x%2Ah%5B2%5D+
+6%2A4+=+x%2Ah%5B2%5D+
+x+=+24%2Fh%5B2%5D+
+x%5E2+=+576%2F%28h%5B2%5D%29%5E2+
+%28h%5B2%5D%29%5E2+ in terms of x%5E2 is
+5%5E2+=+%28x%2F2%29%5E2+%2B+%28h%5B2%5D%29%5E2+
+%28h%5B2%5D%29%5E2+=+25+-+x%5E2%2F4+
and
+x%5E2%2A%2825+-+x%5E2%2F4%29+=+576+
+25x%5E2+-+x%5E4%2F4+=+576+
+x%5E4+-+100x%5E2+%2B+2304+=+0+
Let x%5E2+=+z+
+z%5E2+-+100z+%2B+2304+=+0+
Complete the square
+z%5E2+-+100z+%2B+2500+=+2500+-+2304+
+%28+z+-+50+%29%5E2+=+196+
+z+-+50+=+14+
+z+=+64+
+x%5E2+=+64+
+x+=+8+
x is 8 cm
check answer:
+x+=+24%2Fh%5B2%5D+
+8+=+24%2Fh%5B2%5D+
+h%5B2%5D+=+3+
and
+%28h%5B2%5D%29%5E2+=+25+-+x%5E2%2F4+
+3%5E2+=+25+-+8%5E2%2F4+
+9+=+25+-+64%2F4+
+9+=+25+-+16+
+9+=+9+
OK
and
+%281%2F2%29%2A6%2Ah%5B1%5D+=+%281%2F2%29%2Ax%2Ah%5B2%5D+
+6%2A4+=+8%2A3+
+24+=+24+
OK