PSAT Math : Isosceles Triangles
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Example Question #61 : Triangles
An isosceles triangle has an area of 12. If the ratio of the base to the height is 3:2, what is the length of the two equal sides?
4
6
4√3
5
3√3
5
Area of a triangle is ½ x base x height. Since base:height = 3:2, base = 1.5 height. Area = 12 = ½ x 1.5 height x height or 24/1.5 = height2. Height = 4. Base = 1.5 height = 6. Half the base and the height form the legs of a right triangle, with an equal leg of the isosceles triangle as the hypotenuse. This is a 3-4-5 right triangle.
Example Question #62 : Triangles
Two sides of a triangle each have length 6. All of the following could be the length of the third side EXCEPT
This question is about the Triangle Inequality, which states that in a triangle with two sides A and B, the third side must be greater than the absolute value of the difference between A and B and smaller than the sum of A and B.
Applying the Triangle Inequality to this problem, we see that the third side must be greater than the absolute value of the difference between the other two sides, which is |6-6|=0, and smaller than the sum of the two other sides, which is 6+6=12. The only answer choice that does not satisfy this range of possible values is 12 since the third side must be LESS than 12.
Example Question #3 : Isosceles Triangles
A triangle with two equal angles is called a(n) __________.
disjoint triangle
isosceles triangle
right triangle
Pythagoras triangle
equilateral triangle
isosceles triangle
An isoceles triangle is a triangle that has at least two congruent sides (and therefore, at least two congruent angles as well).
Example Question #1 : Isosceles Triangles
An isosceles triangle has a base of 6 and a height of 4. What is the perimeter of the triangle?
None of these
An isosceles triangle is basically two right triangles stuck together. The isosceles triangle has a base of 6, which means that from the midpoint of the base to one of the angles, the length is 3. Now, you have a right triangle with a base of 3 and a height of 4. The hypotenuse of this right triangle, which is one of the two congruent sides of the isosceles triangle, is 5 units long (according to the Pythagorean Theorem).
The total perimeter will be the length of the base (6) plus the length of the hypotenuse of each right triangle (5).
5 + 5 + 6 = 16
Example Question #5 : 45/45/90 Right Isosceles Triangles
What is the area of a square that has a diagonal whose endpoints in the coordinate plane are located at (-8, 6) and (2, -4)?
100
100√2
200√2
50
50√2
100
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