Question

a trapezoid has bases of lenght 3cm and 7 cm and has legs which are both 4 cm long. how long are it's diagnols? (Show me the process so i can learn TY)

Answer 1

The length of each diagonal is

√((2√3)² + 3²) = √(12 + 9) = √21 cm

See the attachment.

Answer 2

The length of the diagonals of the trapezoid are 10 cm and 4 cm.

Step-by-step explanation:

To find the length of the diagonals of a trapezoid, we can use the Pythagorean theorem. The diagonals of a trapezoid are the hypotenuses of two right triangles formed by connecting the bases and the legs. Let's label the bases as A = 3 cm and B = 7 cm, and the legs as C = D = 4 cm.

The shorter diagonal is the sum of the bases: A + B = 3 cm + 7 cm = 10 cm. The longer diagonal is the difference between the bases: B - A = 7 cm - 3 cm = 4 cm. Therefore, the lengths of the diagonals are 10 cm and 4 cm.