Question

Please solve this question
​

Answer 1

Answer:

AE = 1.15 cm and DE = 2.76 cm

Step-by-step explanation:

Consider the $\triangle{ABC}$ and $\triangle{ADE}$

$\angle BAC = \angle DAE$ (Common angle)

$\angle ABC = \angle ADE$ (Right angle)

$\angle ACB = \angle AED$ (Other two angles of two triangles are same, thus third angle must be same)

Thus, $\triangle{ABC} \sim \triangle{ADE}$  ( By AAA similarity Rule)

Also,we know, when two triangles are similar, then all the corresponding sides are in proportion. Thus we have

$\frac{AB}{AD} = \frac{AC}{AE} = \frac{BC}{DE}$ ----- (1)

Now, we have

AD = 3 cm

DC = 2 cm

BC = 12 cm

AC = AD + DC = 3 + 2 = 5 cm

Also, in right triangle ABC, using Pythagoras theorem, we gave

$AB^2 = AC^2 + BC^2 \\\\ AB^2 = 5^2 + 12^2\\\\ AB^2 = 25 + 144\\\\ AB^2 = 169 \\\\ AB = 13$

Now, using the Eq(1), we have

$\frac{AB}{AD} = \frac{AC}{AE} \\\\ \frac{13}{3} = \frac{5}{AD}\\\\ AD = \frac{5 \times 3}{13}\\\\ AD = \frac{15}{13} \\\\ AD = 1.15cm$

Also, we have

$\frac{AB}{AD} = \frac{BC}{DE} \\\\ \frac{13}{3} = \frac{12}{DE}\\\\ DE = \frac{12 \times 3}{13}\\\\ DE = \frac{36}{13} \\\\ DE = 2.76cm$