If you chose (A), this gives us a value for one side, but we still canвЂ™t determine whether the area is greater than 5 for the entire figure without more information. Since ?3 is more than 1, we know the total area will be more than 5. Now we can see the height is 2, and the base is 2+2?3. Remember the special right triangles ratios! But since itвЂ™s a вЂњyes or noвЂќ question, weвЂ™ll want to solve for the area to see whether it is less than 5.

If this was a вЂњvalueвЂќ question, weвЂ™d be done and not have to actually solve.

Since weвЂ™re dealing with special right triangles, we already know we will be able to move information from one part of the triangle to the other and eventually find the area. If we choose AC as our base, weвЂ™ll need to draw an altitude to create a height.ДЄt a minimum, weвЂ™ll probably need to use BOTH pieces of information given in the statements to try and find both the length of our height AND our base, so letвЂ™s fill that information in:

We know the formula for the area of a triangle is (1/2)(B)(H). ItвЂ™s important to always draw figures that are described but not provided: In triangle ABC, angle ABC is 105 degrees. DonвЂ™t confuse it with the 45-45-90 ratio, and think that the x?3 should be on the hypotenuse! LetвЂ™s check out a sample Veritas Prep question: Remember that for the 30-60-90 triangle, the hypotenuse (longest side) is the side that has the ratio of 2x. Its sides will always be in a ratio of x: x: x?2. The other special triangle is the 45-45-90 triangle. Its sides will always be in a ratio of x: x?3 : 2x. If we know the value of one side, we can find the values of all the other sides. The special right triangles are so called because their side-ratio never changes. Geometry is essential to GMAT Quantitative success, and knowing the special right triangles are a fundamental вЂњyou-will-definitely-see-itвЂќ type of concept. In this triangles we are going to be using the letter вЂњkвЂќ indicating a proportion, for example, if we have the sides вЂњ1kвЂќ and вЂњ2kвЂќ, we can see that the вЂњ2kвЂќ side is double the length of the вЂњ1kвЂќ side, so this is not the actual length of the side but it is the proportion based on the length of the other side.Vivian Kerr is a regular contributor to several GMAT and SAT websites, allowing her to flex her intellectual muscle while she is in between film and stage project as an actress. Another thing important to say is that the bigger the angle is, the longer the opposite side will be.ДЄnother aspect to be clear when we work with special right triangles is that the sum of the three angles will be equals to 180, but as we already know a right triangle has a 90В° angle, this means that the sum of the other 2 angles will be equals to 90В°, this is why when we know the value of an angle we can easily find the other angle just by subtracting the angle we know to 90В°. General properties of the trianglesДЄ reminder before we continue, to name the sides and angles of a triangle, normally we use the letters A, B and C, where the capital letters are used to name the angles and the lowercase letters are used to name sides, where the sides are going to have the same name as the opposite angle. The length of the sides of a triangle cannot be found if we only know the angles, but with the angles we can define the proportion that each side will have, for example, if we have a triangle that has certain angles, based on that we can define that the triangle will have a side that will be 5 units long, other one that will be 4 units long, and the third one will be 3 units long, and this is the basic principle of the special right triangle, not knowing the exact length of the sides of a triangle but knowing the proportions that the sides will have. The special right triangles uses the proportions between the relations of the sides and angles of a right triangle. The special right triangles are triangles that have some established characteristics that allows us to find the sides and angles of the triangle only by taking as reference the proportions of the sides and angles without the need of using the traditional formulas like the trigonometric ratios or the Pythagorean theorem.

What are special right triangles