ISEE Upper Level Quantitative : Right Triangles
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Example Questions
Example Question #71 : Geometry
Figure NOT drawn to scale
Refer to the above diagram, in which 
(a) Four times the area of
(b) Three times the area of
(a) is the greater quantity
It is impossible to determine which is greater from the information given
(a) and (b) are equal
(b) is the greater quantity
(b) is the greater quantity
The altitude of a right triangle from the vertex of its right angle - which, here, is 
making this the similarity ratio. The ratio of the areas of two similar triangles is the square of their similarity ratio, which here is
Therefore, if 
Four times the area of 
Example Question #71 : Geometry
Figure NOT drawn to scale.
Refer to the above diagram, in which
(a) Twice the area of
(b) The area of
(a) is the greater quantity
(a) and (b) are equal
It is impossible to determine which is greater from the information given
(b) is the greater quantity
(b) is the greater quantity
The altitude of a right triangle from the vertex of its right angle - which, here, is 
Because of this, the ratio of the measures of the legs of
Since these legs coincide with the hypotenuses of 
Therefore, the area of 
Example Question #75 : Triangles
The above figure depicts Trapezoid 
(a) The area of
(b) The area of
(b) is the greater quantity
(a) and (b) are equal
It is impossible to determine which is greater from the information given
(a) is the greater quantity
(a) and (b) are equal
The area of a triangle is one half times the product of its height and the length of its base. As can be seen in the diagram below, both 
Since both base length and height are the same between the two triangles, it follows that they have the same area.
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