Question

In the given figure angle:CAB=angleCED CE=10cm,CD=8cm,BE=2cm,AB=9cm,AD=b,DE=a then the value of a+b is

Answer 1

Given: The values angle CAB = angle CED, CE = 10 cm, CD = 8 cm, BE = 2 cm , AB = 9 cm

To find: The value of a+b ?

Solution:

• Now we have given angle CAB = angle CED.

• Consider the triangles ABC and EDC, we get:

                angle ACB = angle DCE            (common angle)

                angle CAB = angle CED            (given)

• So, by AA similarity we can say that triangle ABC similar to triangle DEC.

• Now, we know that ratio of sides of similar triangle are same, so:

                AB/DE = BC/CE = AC/DC

• Now putting the values on above ratio, we get:

                9 / a  =  12 / 10  =  8 + b / 10

• Considering first and second, we get:

                9 / a  =  12 / 10

                9 / a  =  6 / 5

                45 / 6 = a

• Now considering second and third, we get:

                12 / 10  =  8 + b / 10

                6/5 = 8 + b / 10

                60/5 = 8 + b

                60/5 - 8 = b

                b = 60 - 40 / 5

                b = 20 / 5

                b = 4

• So a + b = 45 / 6 + 4 = 45 + 24 / 6

                a + b = 69/6 = 23/2

Answer:

            So the value of a + b is 23/2