Question

What is the value of x?

x=
units

Answer 1

Step 1

In the right triangle RTQ

Find the value of
`RQ^(2)`

Applying the Pythagorean Theorem

`RQ^(2) =RT^(2)+TQ^(2)`

we have

`RT=x\ units \\TQ=16\ units`

substitute the values

`RQ^(2) =x^(2)+16^(2)`

`RQ^(2) =x^(2)+256`

Step 2

In the right triangle RST

Find the value of
`RS^(2)`

Applying the Pythagorean Theorem

`RS^(2) =RT^(2)+ST^(2)`

we have

`RT=x\ units \\ST=9\ units`

substitute the values

`RS^(2) =x^(2)+9^(2)`

`RS^(2)=x^(2)+81`

Step 3

In the right triangle RSQ

Find the value of x

Applying the Pythagorean Theorem

`SQ^(2) =RS^(2)+RQ^(2)`

we have

`RS^(2)=(x^(2)+81)\ units^2\\RQ^(2)=(x^(2)+256)\ units^2`

`SQ^(2)=(16+9)^2=625\ units^2`

substitute the values

`625=(x^(2)+81)+(x^(2)+256)`

`625=(2x^(2)+337)`

`2x^(2)=625-337`

`2x^(2)=288`

`x^(2)=144`

`x=12\ units`

therefore

the answer is

`x=12\ units`