Question

Find the value of x and the value of y

Answer 1

B. y = 4 root under 2, x = 7

B. is the correct answer.

Explanation:

I drew AB such that it is equal and parallel to CD and perpendicular to ED. So, ABCD is a rectangle.

now

triangle ABE is a right angled triangle so

taking 45 as reference angle,

sin45 = p/h

or, sin45 = AB/AE

or, sin45 = 4/y (AB = CD = 4)

or,y = = 4/sin45

`y = (4)/( (1)/( √(2) ) ) \\ y = 4 √(2)`

now

ABCD is a rectangle

BD = AC = 3

in triangle ABE

`y = 4 √(2)`

AB = 4

using pythagoras theorem

h² = p²+b²

or, y² = AB²+ EB²

or,

`{(4 √(2) )}^(2) = {4}^(2) + b`

or, 32 = 16 + EB²

EB² = 16

so, EB = 4

Now

x = EB+BD

= 4+3

so, x = 7