Question

Find the length of the hypotenuse of QPO

Answer 1

`\Huge \boxed{\mathrm{D.} \ 13}`

`\rule[225]{225}{2}`

Explanation:

The triangle is a right triangle.

We can use Pythagorean theorem to solve for the value of x.

`OP^2 +PQ^2 =OQ^2`

`(x+5)^2 +5^2 =(x+6)^2`

Simplifying both sides.

`x^2 +10x+50=x^2 +12x+36`

Subtracting x², 10x and 36 from both sides.

`14=2x`

Dividing both sides by 2.

`7=x`

Letting x = 7 for the length of the hypotenuse.

`\Longrightarrow \ 7+6 \\\\\\ \Longrightarrow \ 13`

`\rule[225]{225}{2}`

Answer 2

The answer is option D

Explanation:

To find the length of the hypotenuse of QPO we must first find the value of x

Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x

Using Pythagoras theorem we have

QO² = QP² + OP²

That's

( x + 6)² = 5² + ( x + 5)²

x² + 12x + 36 = 25 + x² + 10x + 25

Group like terms

x² - x² + 12x - 10x = 50 - 36

2x = 14

Divide both sides by 2

x = 7

The hypotenuse of QPO is (x + 6)

Substitute the value of x into the expression

That's

7 + 6

= 13

Hope this helps you