The lengths of the base of a rectangular table are 7 and 15, and the length of the large leg is 16. 1) Find the length of the middle line of the table. 2) Find the surface area of the table. 3) Find the sharp corner of the table.
Ответы
1) The middle line of a rectangle is the line segment connecting the midpoints of two opposite sides. In this case, it would be the line segment connecting the midpoints of the sides with lengths 7 and 15.
The length of the middle line can be found using the formula: length of the middle line = (1/2) * square root of [(length of side 1)^2 + (length of side 2)^2]
In this case, the length of the middle line = (1/2) * square root [(7^2) + (15^2)] = (1/2) * square root [49 + 225] = (1/2) * square root [274] ≈ 8.29
Therefore, the length of the middle line of the table is approximately 8.29 units.
2) The surface area of a rectangular table can be calculated by multiplying the length and width of the table.
In this case, the length is 15 units and the width is 7 units.
Surface area = length * width = 15 * 7 = 105 square units.
Therefore, the surface area of the table is 105 square units.
3) The sharp corner of the table refers to the vertex where two legs meet. Since the table is rectangular, there are two sharp corners diagonally opposite to each other.
To find the sharp corner, we can use the Pythagorean theorem. Let's label the legs as a = 7, b = 15, and the hypotenuse (long leg) as c = 16.
Using the Pythagorean theorem, a^2 + b^2 = c^2:
7^2 + 15^2 = 49 + 225 = 274.
Therefore, the sharp corner of the table has a length of 16 units.