Question

ABCD is a rectangle with sides 6 cm and

8 cm. If its diagonals cross at X, the length
of AX is​

Answer 1

The length of AX is 5 cm

Explanation:

Diagonal of a Rectangle

Given a rectangle of dimensions W by L (as shown in the image below), the diagonal D is the segment that joins two opposite corners of the rectangle.

The diagonals cross at the center of the rectangle in point X, thus the length of AX is half the length of the diagonal.

Note the diagonal is the hypotenuse of a right triangle with legs W and L, thus:

`D^2=W^2+L^2`

`D^2=6^2+8^2`

`D^2=36+64=100`

`D=√(100)=10`

The length of the diagonal is 10 cm, thus the required distance is AX=10/2 = 5 cm.

The length of AX is 5 cm