Here is Part A of 2 for my question. Here it is:
The lengths of the sides of triangle ABC are 3 cm, 4 cm, and 6 cm. Determine the least possible perimeter of a triangle similar to triangle ABC which has one side of length, 12 cm.
10 points will go to the correct and best answer. If you can show me steps on getting the answer I really appreciate it.
2007-03-28 13:23:28 · 6 answers · asked by poker5495 4 in Science & Mathematics ➔ Mathematics
Find a triangle similar to triangle ABC with the least possible perimeter.
The perimeter of triangle ABC = 3 + 4 + 6 = 13 cm.
The corresponding sides of similar triangles all have the same ratio. So match the 12 cm side to the largest side in triangle ABC. That way the ratio will be as small as possible. In this case:
12/6 = 2
So the perimeter of the triangle similar to triangle ABC is twice as large. The perimeter of the similar triangle is:
2*13 = 26 cm
2007-03-28 13:35:35 · answer #1 · answered by Northstar 7 · 2⤊ 0⤋
A similar triangle will have sides in the same proportions.
Possibilities with a 12 cm side would be 12, 16, 24 (4 times as big)or 9, 12, 18 (3 times as big) or 6, 8, 12 (twice as big).
The smallest perimeter is the last one, which adds up to 26 cm.
2007-03-28 13:32:29 · answer #2 · answered by ewetaunt 3 · 2⤊ 0⤋
Similar is very vague, but anyway--
The longest side on triangle one is 6 cm, the other sides on triangle one are proportional in length by .5 and (2/3) of the longest side. Therefore we will start by making the longest side 12 cm on triangle 2 and using the previous proportions the remaining sides shall be 6 cm & 8cm. (these are .5 and (2/3) of the longest side. The new triangle has the exact ratio with respect to demnsions and has a perimeter of 26cm.
2007-03-28 13:32:38 · answer #3 · answered by cage 1 · 2⤊ 0⤋
For the smallest perimeter, the other sides must be 6cm and 8cm, as it's similar. So the smallest possible perimeter is 6+8+12 = 26 cm.
2007-03-28 13:34:02 · answer #4 · answered by Anonymous · 2⤊ 0⤋
Similar triangles involve ratios...so, the sides should be 6, 8, and 12. The ratios are the same.
2007-03-28 13:29:43 · answer #5 · answered by Anonymous · 1⤊ 0⤋
Assuming T is the top factor of the attitude, and ok is the decrease: Draw a line phase between T and ok. (word: This basically works if TK is perpendicular to the precise line) attitude KTD(vertex T) is ninety-38=fifty two ranges attitude DKT(vertex ok) is90-31=fifty 9 ranges upload up the measures:fifty two+fifty 9=111 ranges one hundred eighty-111=sixty 9 ranges
2016-11-24 20:28:48 · answer #6 · answered by ? 4 · 0⤊ 0⤋