square inside triangle / isosc. trapezium / midpts of triang

[nopainnogain]

Do you know how to solve these problems? If so, please reply.

1) What is the length of a side of a square inscribed in a right angled triangle with one of its sides lying on the hypotenuse? The sides of the triangle are 15, 12, and nine units.

2) An isosceles trapezium is ________ quadrilateral.

3) A line joining the mid-points of a pair of sides of a triangle is 40 sq units is drawn. The smaller triangle so formed is cut off. The area of the resulting trapezium is _______.

 

[stapel]

1) What is the length of a side of a square inscribed in a right angled triangle with one of its sides lying on the hypotenuse? The sides of the triangle are 15, 12, and nine units.

You've drawn the triangle and the inscribed square, labelled the sides of the triangle with their various lengths, noted the various similar triangles, set up the ratios and proportions, and... then what?

2) An isosceles trapezium is ________ quadrilateral.

This is a vocabulary question. Flip through your book and/or your class notes to find the expected term.

3) A line joining the mid-points of a pair of sides of a triangle is 40 sq units is drawn. The smaller triangle so formed is cut off. The area of the resulting trapezium is _______.

Without the drawing, I'm afraid there is no way to find the answer. Please consult with your instructor regarding this missing information. (I understand that you would have included this information, or at least a detailed description of it, had it been made available to you.)

When you reply, please include a clear listing of everything you have tried so far. Thank you!

Eliz.

 

[TchrWill]

1) What is the length of a side of a square inscribed in a right angled triangle with one of its sides lying on the hypotenuse? The sides of the triangle are 15, 12, and nine units.

It helps to draw a figure first.

Draw the triangle with the enclosed square letting the side of the square be x.

In drawing the square within the triangle, how many other triangles are formed?

Are there any similar triangle in the resulting figure?

If yes, how can you express the length of the hypotenuse in terms of x?