Question

Sofia cuts a piece of felt in the shape of a kite for an art project. The top two sides measure 20 cm each and the bottom two sides measure 13 cm each. One diagonal, EG, measures 24 cm.What is the length of the other diagonal, DF?5 cm16 cm21 cm32 cm

Answer 1

In geometry, it is always advantageous to draw a diagram from the given information in order to visualize the problem in the context of the given.

A figure has been drawn to define the vertices and intersections.

The given lengths are also noted.

From the properties of a kite, the diagonals intersect at right angles, resulting in four right triangles.

Since we know two of the sides of each of the right triangles, we can calculate their heights which in turn are the segments which make up the other diagonal.

From triangle A F G, we use Pythagoras theorem to find

h1=A F=sqrt(20*20-12*12)=sqrt(256)=16

From triangle DFG, we use Pythagoras theorem to find

h2=DF=sqrt(13*13-12*12)=sqrt(25) = 5

So the length of the other diagonal equals 16+5=21 cm