Give 5 examples of rectangles whose sidelengths and diagonals are all integers. Class 8

Give 5 examples of rectangles whose sidelengths and diagonals are all integers. Class 8

Question 1.

Give 5 examples of rectangles whose sidelengths and diagonals are all integers. Class 8

Solution:

3 cm, 4 cm and 5 cm; 5 cm, 12 cm and 13 cm; 7 cm, 24 cm and 25 cm; 6 cm, 10 cm and 15 cm; 10 cm, 24 cm and 26 cm.

Question 2.

Construct a square whose area is equal to the difference of the areas of squares of sidelengths 5 units and 7 units. Class 8

Solution:

First construct a right triangle ABC with hypotenuse AC = 7 cm and side AB = 5 cm.

Now, draw a square with one side as BC as shown.

Then, BCDE is the required square whose area is equal to difference of areas of squares of sidelength 5 units and 7 units.