damien made a symmetrical origami fox using a right-angled triangular paper aed. ae = ed = 14 cm and be = ce. the area of triangle bce is 2 times that of triangle cde. he then folded the 2 corners of the triangle to the back and formed the fox below. after folding, of triangle cde was hidden. What is the ratio of the area of triangle DCG to the area of triangle BCE?

Answer 1

Let x be the length of BE = CE.

Since triangle BCE is congruent to triangle CDE, and the area of triangle BCE is 2 times that of triangle CDE, we can set up the following equation:

(1/2)(14)(x) = 2(1/2)(14)(14) = 196
7x = 196
x = 28

Since BE = CE = 28, then triangle BCE is an isosceles right triangle with legs of length 28, and therefore the area of triangle BCE is (1/2)(28)(28) = 392.

After folding, the hidden triangle DCG is congruent to triangle BCE, since they are mirror images of each other after folding.

Therefore, the area of triangle DCG is also 392.

The ratio of the area of triangle DCG to the area of triangle BCE is:

392/392 = 1

Therefore, the ratio of the area of triangle DCG to the area of triangle BCE is 1:1.