Triangles BCD and GHI are similar. THe length of sides BCD are 17x-49, 2x+224, and 14+13x. Perimeter of BCD is 861. The length of the smallest side of GHI is 169+x. What is the length of the longest side of GHI?
2006-09-17 13:48:08 · 2 answers · asked by yeahh...umm... its me! 1 in Science & Mathematics ➔ Mathematics
The perimeter of BCD equals the sum of the lengths of the sides.
Hence, (17x-49) + (2x+224) + (14 + 13x) = 861.
32x = 189
x = (189/32)
Plug that x-value into the equations for each side of BCD, to figure out which side is shortest and which is longest.
The ratio of shortest-to-longest for BCD will be the same as the ratio of shortest-to-longest for GHI. You can compute the length of the shortest side of GHI using the 169+x formula.
That should be enough information for you to solve the problem!
2006-09-17 13:55:06 · answer #1 · answered by Bramblyspam 7 · 0⤊ 0⤋
Perimeter of BCD=17x-49 +2x +224 +14 +13x =861
32x+189 =861
32x =672
x =21
Sides of BCD are 308, 266, 287
The smallest side of BCD=266.................i
Smallest side of GHI = 169 +21=190..........ii
Ratio =190/266=0.714285714
Length of the longest side of GHI =308x190/266=220
2006-09-17 14:56:40 · answer #2 · answered by Amar Soni 7 · 0⤊ 0⤋