If side RQ has length 6, then the sides have length 6, 6, and 2.
Since PQR is an isosceles triangle, the third side (RQ) must have length 6 or 2 (so that we have two sides of equal length). Statement 2 tells us that one side has length 2 Statement 1 tells us that one side has length 6 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENTĪpplying the same logic we used for statement 1, we can see that statement 2 is NOT SUFFICIENT In this case, the perimeter = 6 + 6 + 4 = 16 Note that this is an isosceles triangle AND it meets the above rule. In this case, the perimeter = 6 + 6 + 5 = 17Ĭase b: Case a: PQ = 6, PR = 6 and RQ = 4. Here are two:Ĭase a: PQ = 6, PR = 6 and RQ = 5. There are many isosceles triangles that satisfy statement 1.
Target question: What is the perimeter of isosceles triangle PQR? ĭIFFERENCE between A and B < length of third side < SUM of A and B IMPORTANT RULE: If two sides of a triangle have lengths A and B, then. So the answer to the question is still C but the perimeter of our triangle will be 6+6+2 = 14. However, a triangle with sides 6, 6, 2 is definitely possible, because in this sum of any two sides is greater than the third side. If you try to construct a Triangle with these sides, you wont be able to. On this basis, a triangle with sides 2, 2, 6 is Not possible because 2+2 is not greater than 6. Next, triangle inequality is an important property of Every triangle - according to which sum of any two sides of a triangle MUST be greater than the third side, and similarly difference of any two sides of a triangle MUST be less than the third side. Only Right Angled Isosceles triangle (with angles 45, 45 and 90 degrees) has this ratio of sides as 1:1:root 2 I believe i went seriously wrong somewhereįirst of all, NOT every isosceles triangle has sides in the ratio 1:1:root 2. So the sides should be 2,2,6 so perimeter is 10. Obvisously we cannot have 6 and 6 as two sides because the third side has to be greater than 6 and we got the third side a 2. Instead of starting with side c< side a+b, i started like lsosceles triangle will have sides in ratio 1:1:root 2.
Ans C.ġ and 2 are not sufficient clearly, so 1+2 So we can assure our triangle has a perimeter of 6+6+2. So the sum of two of the 3 sides of a triangle must be always greater than the length of the other one and in this case, this is not satified. If we had 2,2 and 6 we could NOT form a triangle because the shortest distance between two points is the straight line. If we had 6,6 and 2, the equilateral triangle would have a perimeter of 14. The third side must be equal to one of the mentioned sides. NOT SUFFICIENT.Ĭombining the statements we are given two sides of the equilateral triangle 2 and 6. NOT SUFFICIENT.Ģ) Statement 2 Same as the above and the combinations are again infinite 2,7,7 2,2,1. Considering that an isósceles triangle has at least 2 same sized sides we have infinite combinations and posibilities 6,6,1 6,5,5 6,6,6. What is its perimeter?ġ) Statement 1 tells us that one of the sides is = 6, but we do not have information about the other sides.
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