In the fig DE BC, AD= 2.4cm, BD = 7.2 cm , AE = 1.8cm then length of AC is
Answers
Answer:
7.2cm
Step-by-step explanation:
Given,
DE ║ BC
AD = 2.4cm
BD = 7.2cm
AE = 1.8cm
To Find :-
Value of 'AC'.
Solution :-
In Δ ADE , ΔABC :-
∠ADE = ∠ABC
[ ∴ Corresponding angles are equal ]
∠AED = ∠ACB
[ ∴ Corresponding angles are equal ]
→ We can say that :-
∠ADB ≅ ∠AEC
→ AD/AB = AE/AC
[ ∴ Corresponding sides are proportional ]
Finding value of AB :-
AB = AD + DB
= 2.4cm + 7.2cm
= 9.6cm
∴AB = 9.6cm
Finding value of 'AC' :-
AC = AE + EC
= 1.8cm + EC
∴AC = 1.8cm + EC
Substituting in the formula :-
2.4cm/9.6cm = 1.8cm/1.8cm + EC
cross multiplying :-
2.4cm(1.8cm + EC) = 1.8cm(9.6cm)
2.4cm(1.8cm + EC) = 17.28cm²
1.8cm + EC = 17.28cm²/2.4cm
1.8cm + EC = 7.2cm
EC = 7.2cm - 1.8cm
EC = 5.4cm
∴ EC = 5.4cm
AC = AE + EC
= 1.8cm + 5.4cm
= 7.2cm
∴AC = 7.2cm.
Formulas Used :-
1) Corresponding angles are equal
2) Corresponding sides are proportional
Note : refer to above attachment
Step-by-step explanation:
hope you find it helpfull
