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Only 3: [1,4,4], [2,3,4] and [3,3,3]

Remeber that the sum of the lengths of any two sides MUST be greater than the third side. So triangles like [1,2,6] cannot exist.

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Q: How many triangles with integer sides are there where its perimeter is 9cm's?
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Which animals fall under insects?

There are well over 1 million different known species of insects in the world,and some experts estimate that there might be as many as 10 million.All these species are divided up into about 32 orders, depending on whose taxonomic system you use, of which, the largest is the Beetles, or Coleoptera, with 125 different families and around 500,000 species they are an incredibly diverse group of animals. In fact, one in every four animal species on this planet is a beetle.Well, everywhere on land anyway, very few insects have colonised the sea, though some like the Marine Flies (Halobates sp.) and the Seashore Collembolan, Anurida maritma, live on the surface. Also the larva of a small number of True Flies (Diptera) and Beetles (Coleoptera) live beneath the surface, mostly in rockpools.On the land however there isn't anyhere you can go that you can't find some insects, even in the frozen extremes of Arctica and Antarctica you will find some insects alive and active during the warmer months.You will find that insects are ubiquitous, they are in the soil beneath your feet, in the air above your head, on and in the bodies of the plants and animals around you, as well as on and in you.Some of the most adventurous insect are the Brine Flies (Ephydra), you can find them living in the strangest places including, the larva of Ephydra hyans in Mono Lake California which is nearly as salty as the Dead Sea, the larva of Psilopa petrolei in pools of crude oil also in California, and the adults and larva of Scatella thermarum in the hot springs of Iceland, the adults live on the mats of algae which float on the water's surface, and the larva live beneath the mats and in water, which is as hot as 48 degrees Celsius, which, for most people, is too hot to put your hand into.There are several different ways of measuring the size of an insect, most people would consider the largest insect to be the bulkiest, in this case the champion insect is the Acteon Beetle (Megasoma acteon) from South America the males of which can be 9cms long by 5cms wide by 4cms thick, however there is a serious challange for heaviest insect in the world in the form of the True Wetas from New Zealand. For instance a gravid female Deinacrida heteracantha can weigh as much as 70 grams.Another competitor for the title is the extemely rare South American Longhorn Beetle Titanus giganteus, these giants can have a body length (not including antennae) of over 16cms (6.5 ins), other longhorn beetles are nearly as large and may look even bigger because of their longer legs i.e. Xixuthrus herosfrom Fiji. Another beetle, Dynastes Hercules is also well known for reaching 16cms in length, though it is not nearly a heavy.However other insects are larger in other ways, the longest insect in the world is the Stick-Insect Pharnacia kirbyi, the females of which can be over 36cm long. Some living lepidoptera have wingspans as great as 32cm and an area of over 300 square cms.There are an incredible number of very small insects in the world, far more than there are giants. Many beetles are less than one millimetre in length, and the North American Feather-winged Beetle Nanosella fungi, at 0.25mm, is a serious contender for the title of smallest insect in the world. Other insect orders which contain extremely small members are the Diptera (True Flies) and the Collembola (Springtails).There are also many small Hymenoptera, especially in the Superfamily Chalcidoidea, such as the Fairy Flies, of the family Myrmaridae, of which Alaptus magnanimus, at 0.21mm long, was once thought to be the smallest insects in the world. However another Hymenopteran parasite now holds the record. Megaphragma caribea from Guadeloupe, measuring out at a huge 0.17 mm long, is now probably the smallest known insect in the world.The incredible size of individual species of insects is only dwarfed by the incredible numbers they sometimes occur in. In 1943 Profeesor Salt found that an acre of British pastureland near Cambridge supported over 1,000,000,000 Arthropods of which nearly 400,000,000 were Insects and 666,000,000 were Mites the remaining 38,000,000 were Myriapods (Centipedes and Millipedes).Some Scientist have recorded the otherwise inconspicous Springtails at densities as high 100,000,000 per square metre in the ordinary farm soil of Iowa U.S.A.In Africa swarms of Orthoptera ( Desert Locusts Schistocerca gregaria) may contain as many as 28,000,000,000 individuals. Although each Locust only weighs about 2.5grams when they are all added up together this comes to 70,000 tons of locust.Ants are social animals and live in colonies, sometimes these colonies may contain only 50 or so individuals, but, one supercolony of Formica yessensis on the coast of Japan is reported to have had 1,080,000 queensand 306,000,000 workers in 45,000 interconnected nests.Some Scientist think that 30% of the animal biomass of the Amazon Basin is made up of ants,and that:-- 10% of the animal biomass of the world is ants,furthermore they believe another 10% is composed of Termites.This means that 'social insects'could make up an incredible 20%of the total animal biomass of this planet.What Is a Mammal?Humans are mammals. The word mammal comes from the Latin mamma, meaning breast, because female mammals produce milk to nurse their babies. Nearly all mammals give birth to live young, and all are warmblooded, maintaining a near-constant body temperature regardless of environmental conditions. They are vertebrates and use lungs to breathe air and are the only animals that grow hair. Mammals probably appeared on Earth some 200 million years ago.This answer was plagiarized from http://earthlife.net/insects/six01.HTML