PS-Geometry

PS Questions of Geometry

What is the area of the triangle in the figure above?
CONCEPT: Area of a triangle = (1/2)* a* b* sin (angle included between a and b) where  a and b are two sides of the triangle. SOLUTION: The sine formula f...
Tue, 12 Oct, 2021 at 2:09 PM
The rectangle and the parallelogram pictured below have the same perimeters. What is the length of side EF?
CONCEPT: The question tests on the basics of Geometry SOLUTION:   Perimeter of the rectangle = 2*(L+B) = 2*(8+5)=26 units Given, the parallelogram has the ...
Tue, 12 Oct, 2021 at 2:10 PM
In the xy-plane, which of the following (x,y) pairs defines a point that lies on the same line as the two points defined by the pairs (2,3) and (4,1)?
CONCEPT: The question is from the area of coordinate Geometry SOLUTION: Slope of the line =y2-y1/x2-x1 = 1-3/(4-2) = -1 Substitute (x, y) for both point to...
Tue, 12 Oct, 2021 at 2:10 PM
The figure below shows an equilateral triangle (∆ABC) tangent to circle O at three points. If the perimeter of ∆ABC is 18, the area of circle O =
CONCEPT: The question tests the basics of Mensuration and Geometry SOLUTION: The in-radius of an equilateral triangle is √3 * (side) /6 (In-radius is 1/3 ...
Tue, 12 Oct, 2021 at 2:10 PM
In the xy-plane, at what point along the y-axis does the line passing through points (5,–2) and (3,4) intersect that axis?
CONCEPT: The question tests the areas of coordinate geometry SOLUTION: The eqn of the line => y-y1/x-x1= y2-y1/x2-x1 We get y-(-2)/x-5 = 4-(-2)/3-5 =&g...
Tue, 12 Oct, 2021 at 2:10 PM
In the triangle shown below, what is the value of x ?
CONCEPT: The question tests on the basics of Geometry SOLUTION:   In the given triangle sin 45 =perpendicular / hypotneuse => 1/√2 = √2 /x =>x = 2 (O...
Tue, 12 Oct, 2021 at 2:10 PM
In the triangle shown below, what is the value of x ?
CONCEPT: The question tests on the basics of Geometry SOLUTION:   In the given triangle, sin 30 =perpendicular/hypotenuse =>1/2 = x/10  =>x=5 units (...
Tue, 12 Oct, 2021 at 2:10 PM
What is the area of the triangle shown below?
CONCEPT: The question tests on the basics of Geometry SOLUTION: This is a 30-60-90 triangle , its side lengths are always in the ratio of 1: √3: 2. [a: 3√...
Tue, 12 Oct, 2021 at 2:10 PM
In the xy-plane, what is the slope of the line defined by the two points P(2,1) and Q(–3,4)?
CONCEPT: The question tests on the basics of Coordinate Geometry SOLUTION:   Given: (x1,y1)=(2,1) (x2,y2)=(-3,4) Slope for (x1,y1) and (x2,y2) = (y2-y1)/(...
Tue, 12 Oct, 2021 at 2:11 PM
Two rectangles have the same area. One is twice as long as the other. If the longer rectangle has a length of L and a width of W, what is the perimeter of the shorter rectangle?
  SOLUTION: Rectangle 1(Longer Rectangle): Length(L1)= L and Width(W1)=W Rectangle 2: Length(L2) = L/2 Areas being same L*W1 = (L/2)* W2 =>LW=(L/2...
Tue, 12 Oct, 2021 at 2:11 PM