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 cm 16 cm 21 cm 32 cm

Answer 1

Answer:

(C) 21 cm

Step-by-step explanation:

It is given that AEBG is a kite in which AE=AG=20cm and EB=BG=13 cm and FG=24 cm.

Now, from ΔCBG, we have

$(BG)^2=(CG)^2+(CB)^2$

$(13)^2=(12)^2+(CB)^2$

$169-144=(CB)^2$

$25=(CB)^2$

$5 cm=CB$

Also, from ΔACG, we have

$(AG)^2=(CG)^2+(AC)^2$

$(20)^2=(12)^2+(AC)^2$

$400-144=(AC)^2$

$256=(AC)^2$

$16 cm=AC$

Now, the length of the other diagonal is given as:

$AB=AC+CB$

Substituting the given values, we have

$AB=16+5$

$AB=21 cm$

Therefore, the value of the other diagonal is 21 cm, hence option C is correct.

Answer 2

Use the Pythagorean theorem( a squared+b squared= c squared) to get the separate segments of FD. 16+5= 21. Your answer is C, 21 cm.