Advertisements
Advertisements
प्रश्न
In the adjacent figure, ∆ABC is right angled at C and DE ⊥ AB. Prove that ∆ABC ~ ∆ADE and hence find the lengths of AE and DE
उत्तर
In ∆ABC and ∆ADE
∠ACB = ∠AED = 90°
∠A = ∠A ...(common)
∴ ∆ABC ~ ∆ADE ...(By AA similarity)
`"BC"/"DE" = "AB"/"AD" = "AC"/"AE"`
`12/"DE" = 13/3 = 5/"AE"`
In ∆ABC, AB2 = BC2 + AC2
= 122 + 52
= 144 + 25
= 169
AB = `sqrt(169)` = 13
Consider, `13/3 = 5/"AE"`
∴ AE = `(5 xx 3)/13 = 15/13`
AE = `15/13` and DE = `36/13`
Consider, `12/"DE" = 13/3`
DE = `(12 xx 3)/13 = 36/13`
APPEARS IN
संबंधित प्रश्न
In figure, ∠BAC = 90º and segment AD ⊥ BC. Prove that AD2 = BD × DC.
In the given figure, ∆ABC and ∆AMP are right angled at B and M respectively.
Given AC = 10 cm, AP = 15 cm and PM = 12 cm.
- Prove that: ∆ABC ~ ∆AMP
- Find: AB and BC.
In each of the given pairs of triangles, find which pair of triangles are similar. State the similarity criterion and write the similarity relation in symbolic form:
ΔABC ~ ΔDEF and their areas are respectively `100cm^2` and `49cm2`. If the altitude of ΔABC is 5cm, find the corresponding altitude of ΔDEF.
In Δ ABC , DE is parallel to BC and `"AD"/"DB" = 2/7` IF AC = 5 .6 , find AE.
In the following figure, point D divides AB in the ratio 3 : 5. Find : `(AD)/(AB)`
In the following figure, point D divides AB in the ratio 3 : 5. Find :
BC = 4.8 cm, find the length of DE.
In ΔABC, D and E are the mid-point on AB and AC such that DE || BC.
If AD : BD = 4 : 5 and EC = 2.5cm, find AE.
ΔPQR ~ ΔSUV. Write pairs of congruent angles
In ΔABC, PQ || BC. If PB = 6 cm, AP = 4 cm, AQ = 8 cm, find the length of AC.
