Question

In CED= CAB
Find the value of x​

Answer 1

Answer:

$\huge{ANSWER}$

Step-by-step explanation:

Given,

angle A = angle CED

AB = 9cm , CE = 10 cm , DC = 8cm , BE = 2cm , DE = x , AD = 7 cm

Now,

In ∆CAB and ∆CED

where angle C is equal to( = ) angle C

angle C = angle C { common }

angle A = angle CED--------{given}

•°• ∆CAD ~ ∆CED -----{ by AA similarity }

$\frac{ca}{ce} = \frac{ab}{de} = \frac{cb}{cd}$

( note: these are in capitals write it in capitals in your copy)

$\frac{ab}{de} = \frac{cb}{cd}$

_____( since we provide above that corresponding sides of the two similar triangle are proportional)

$\frac{9}{x} = \frac{ce \: + \: eb}{cd}$

$\frac{9}{x} = \frac{(10 + 2)}{8}$

$\frac{9}{x} = \frac{12}{8}$

$12x = 8 \times 9 \\ x = \frac{8 \times 9}{12} \\ \\ x = \frac{2 \times 9}{3} \\ x = 2 \times 3 \\ x = 6cm$

Hence the Value of $\huge{x}$ is $\huge{6cm}$

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