Question

-In Fig. 2, IF DE || BC, then x equals
(a) 6 cm
(b) 8 cm
(c) 10 cm
(d) 12.5
​

Answer 1

❏ Question:-

If DE||BC then find the value of x

$\setlength{\unitlength}{1 cm}\begin{picture}(12,4)\thicklines\put(4.8,6){ . }\put(5.6,5.9){ B }\put(10.2,5.9){ C }\put(7.8,10.2){ A }\put(6.6,7.9){ D }\put(9.08,7.9){ E }\put(7.7,7.7){ 4\:cm }\put(7.7,5.7){ x\:cm }\put(6.6,9){ 2\:cm }\put(5.7,7){ 3\:cm }\put(6,6){\line(1,0){4}}\put(7,8){\line(1,0){2}}\put(6,6){\line(1,2){2}}\put(10,6){\line(-1,2){2}}\end{picture}$

options:-

(a)6 cm

(b)8 cm

(c)10 cm

(d)12.5 cm

❏ Solution:-

✏ Given:-

• DE||BC
• AD=2 cm
• BD=3 cm
• DE=4 cm
• BC=x cm.

✏ To Find:-

• value of x = ?

✏ Explanation :-

$\setlength{\unitlength}{1 cm}\begin{picture}(12,4)\thicklines\put(4.8,6){ . }\put(5.6,5.9){ B }\put(10.2,5.9){ C }\put(7.8,10.2){ A }\put(6.6,7.9){ D }\put(9.08,7.9){ E }\put(6.6,9){ a\:cm }\put(5.7,7){ b\:cm }\put(6,6){\line(1,0){4}}\put(7,8){\line(1,0){2}}\put(6,6){\line(1,2){2}}\put(10,6){\line(-1,2){2}}\end{picture}$

Now, We know that ,

$\sf\implies DE=\frac{a}{a+b}\times BC$

here, DE=4 cm ; a=2 cm ; b=3 cm ;

∴ Value of BC,

$\sf\implies 4=\frac{2}{2+3}\times BC$

$\sf\implies 4\times5=2\times BC$

$\sf\implies \frac{\cancel{20}}{\cancel2}=BC$

$\sf\implies \boxed{\large{\red{BC=x= 10 \:cm}}}$

∴ The value of x = 10 cm.

➩ option (C) 10 cm.

Answer 2

Answer:

(c)10cm

Step-by-step explanation:

$given$

1. DE//BC
2. AD=2cm
3. BD=3cm
4. DE=4cm

$to \: find \: \: x$

Solutions;

∆ADE and ∆ABC

angle A = angle A (common)

ANGLE ADE = ANGLE ABC

∆ADE ~ ∆ABC

In photo