Question

5. What are the values of x and y?

O x=2sqrt3 y=4
O x=8sqrt7 y=4sqrt21
O x=8sqrt3 y=8sqrt3
O x=4sqrt21 y=8sqrt7​

Answer 1

x= 90 degree

y= 43 degree

Explanation:

We have been given an isosceles triangle being two sides equal AB and AC

By the property of isosceles triangle

The sides which are equal will have same base angle

Hence, ∠ABC=∠ACB=

We know that sum of angles of triangle is

∠ABC+ ∠ACB+∠BAC= (1)

Since, ∠BAC is the bisector so, ∠BAD and ∠DAC are equal which is

Now, substituting the values in (1) we get:

Now, we will consider ΔABD to find x

,∠ADB=∠ABD=

Now, Apply the sum of angles of triangle is we get:

Answer 2

x = 8
`√(7)`

y = 4
`√(21)`

Explanation:

use the altitude rule to find the height of the triangle first

12/h = h/16

h² = 12x16

h =
`√(192)`

h =
`√(4)`
`√(4)`
`√(4)`
`√(3)` = 8
`√(3)`

now you can use the Pythagorean Theorem with height of 8
`√(3)` along with the other leg of 12 to find 'y'; which comes out to be
`√(336)` or
`√(4)`
`√(4)`
`√(21)`

then use the Pythagorean Theorem with height of 8
`√(3)` along with the other leg of 16 to find 'x'; which comes out to be
`√(448)` or
`√(4)`
`√(4)`
`√(4)`
`√(7)`