Question

AD=17 AB=10 BC=15 angle ABC= angle BCD =90° seg AB parpindicular to side CD then find the length of AE DC DE​

Answer 1

Answer:

ABCE is a rectangle

so AE = 15

by Pythagoras theorem

in triangle ADE

(DE)^2 = (AD)^2 - ( AE)^2

DE^2 = 289-225

DE^2 = 64

DE = 8

DC= DE+EC

DC = 8 + 10

DC= 18

Answer 2

Given:

• AD = 17 cm
• AB = 10 cm
• BC = 15 cm
• ∠ABC = ∠BCD = 90°
• AB ⊥ CD

To Find:

• The length of AE, DC, and DE

Solution:

• Since ABCE is a rectangle.
• BC = AE (∵ Opposite sides of a rectangle are equal)
• AE = 15 cm
• Consider ΔADE,
• Applying Pythagoras theorem, $DE^2 = AD^2-AE^2$
• Substituting the values we get,
• $DE^2 = 17^2 - 15^2$
• $DE^2$  = 289 - 225 = 64
• DE = √64 = 8 cm
• Now from the figure,
• DC = DE + EC
• DC = 8 + 10 ( AB = EC)
• DC = 18 cm

∴ The length of AE = 15 cm, DC = 18 cm, and DE = 8 cm.