Question

What is the value of X

Answer 1

The value of x is 12 cm.

Explanation:

From the given figure, we know that the two corresponding lines are parallel and so the two given triangles are congruent to each other.

Therefore, the corresponding sides of these triangles will also be proportional so we can write it as:

`(4)/(4+16) =(3)/(3+x)`

`(4)/(20) =(3)/(3+x)`

By cross multiplication:

`12+4x=60`

`4x=60-12`

`4x=48`

`x=(48)/(4)`

`x=12`

Therefore, the value of x is 12 cm.

Answer 2

`x=12`

Explanation:

We have been given a graph of similar triangles. We are asked to find the value of x.

Since we know that corresponding sides of similar triangles are always in same proportion, so we will use proportions to find the length of x.

`(3)/(x+3)=(4)/(16+4)`

`(3)/(x+3)=(4)/(20)`

Upon cross multiplying our equation we will get,

`4*(x+3)=3(20)`

Upon distributing 4 we will get,

`4x+12=60`

Let us subtract 12 from both sides of our equation.

`4x+12-12=60-12`

`4x=48`

Upon dividing both sides of our equation by 4 we will get,

`(4x)/(4)=(48)/(4)`

`x=12`

Therefore, the value of x will be 12.