Similar Triangles, 3

Category: Plane Geometry

"Published in Newark, California, USA"

In the given figure below, a segment joins the midpoints of two sides of a triangle. Find the values of x and y.

Photo by Math Principles in Everyday Life

Solution:

Consider the given figure above

Photo by Math Principles in Everyday Life

Since a line segment joins the midpoints of two sides of a triangle, then the value of y is
 

 

 

 

A small triangle is similar to big triangle because a line segment which is its base that joins the midpoints of two sides of a big triangle is parallel to the base of big triangle. By similar triangles, the value of x is

Square, Rectangle, and Parallelogram Problems, 18

Category: Plane Geometry

"Published in Vacaville, California, USA"

A parcel of land is 6 ft longer than it is wide. Each diagonal from one corner to the opposite corner is 174 ft long. What are the dimensions of the parcel?

Solution:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life

Since the two diagonals of a parcel are equal, then the parcel is a rectangle in which all sides are perpendicular to each other. If the diagonal is given, then we can solve for the width of a rectangle by Pythagorean Theorem as follows

By completing the square method,

Since the dimensions of a rectangle are all positive values, then we have to choose the positive sign. Hence, the width of a rectangle is

and the length of a rectangle is .

Therefore, the dimensions of a parcel of land are 120 ft by 126 ft.  

Square, Rectangle, and Parallelogram Problems, 17

Category: Plane Geometry

"Published in Vacaville, California, USA"

A rectangular garden is 10 ft longer than its wide. Its area is 875 ft². What are its dimensions?

Solution:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life

The area of a rectangle is 

Substitute the values of area, length, and width to the above equation in order to solve for the value of x, we have
 

 

By completing the square method,

 

 

 

 

 

 

Since the dimensions of a rectangle are all positive values, then we have to choose the positive sign. Hence, the width of a rectangle is
 

 

 

and the length of a rectangle is  .

Therefore, the dimensions of a rectangular garden are 25 ft by 35 ft.