2.10  Theorem of Pythagoras

To see Section 2.10, with detailed explanations, examples, exercises, and answers, click here! 

Regretfully, I still cannot draw pictures for this webpage.  Therefore, you will have to draw and label the rectangles and triangles for each problem here.

41.     Find the width of a rectangle whose diagonal is and length is  

Solution:    Let = the width of the rectangle.

                             = the length of the rectangle.

                             = the diagonal of the rectangle.

Draw a rectangle with a diagonal, which will divide the rectangle into two triangles.  The legs of the triangle are and , and the hypotenuse is .

In order to get all the number terms on the right side, subtract  from each side:

Take the square root of each side:

Of course, the negative answer is rejected, since the side of a rectangle cannot be negative. 

Final answer:     

42.     Find the width of a rectangle whose diagonal is and length is  

Solution:    Let = the width of the rectangle.

                             = the length of the rectangle.

                             = the diagonal of the rectangle.

Draw a rectangle with a diagonal, which will divide the rectangle into two triangles.  The legs of the triangle are and , and the hypotenuse is .

In order to get all the number  terms on the right side, subtract  from each side:

Take the square root of each side:

Of course, the negative answer is rejected, since the side of a rectangle cannot be negative. 

Final answer:     

45.     A guy wire to the top of a  pole reaches the ground  from the base of the pole. How long is the wire?

Solution:    Let   = the length of the wire.

                             = the height of the pole.

                             = the base of the triangle.

Draw a right triangle with base  and height .  The hypotenuse will be the length of the wire, which is .  The legs of the triangle are and , and the hypotenuse is .

Combine the number  terms on the left side:

Take the square root of each side:

Use a calculator and round to the nearest hundredth:

The negative answer is rejected, since the side of a triangle cannot be negative. 

Final answer:             

46.     A guy wire to the top of a pole is long.  It reaches the ground  from the base of the pole. How tall is the pole?

Solution:    Let   = the height of the pole.

                             = the length of the wire.

                             = the base of the triangle.

Draw a right triangle with base  and height .  The hypotenuse will be the length of the wire, which is .  The legs of the triangle are and , and the hypotenuse is .

Subtract from each side:

Take the square root of each side:

Use a calculator and round to the nearest hundredth:

The negative answer is rejected, since the side of a triangle cannot be negative. 

Final answer:             

Return to main page       Return to Basic Algebra      Math in Living C O L O R !!