Question

Find the values of x and y.

Answer 1

`x=3.5,y=24`

Explanation:

The smaller triangle joining the midpoints of the bigger right angle triangle will also be a right angle triangle.

Midpoint Theorem-

According to this, the segment joining two sides of a triangle at the midpoints is half the length of the third side.

Applying this,

`\Rightarrow x=(1)/(2)(4x-7)`

`\Rightarrow 2x=4x-7`

`\Rightarrow 4x-2x=7`

`\Rightarrow 2x=7`

`\Rightarrow x=(7)/(2)=3.5`

So, the hypotenuses of the bigger triangle will be,

`=6(3.5)+4=25`

Applying the mid point theorem, the hypotenuses of the smaller triangle will be,

`=(1)/(2)* 25=12.5`

Applying Pythagoras theorem in the smaller triangle, the leg will be

`=√(12.5^2-3.5^2)\\\\=√(156.25-12.25)\\\\=√(144)\\\\=12`

Again applying mid point theorem,

`\Rightarrow y=2* 12=24`