Find the length of the hypotenuse of QPO

Step-by-step 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

Hope this helps you

Step-by-step explanation:

The triangle is a right triangle.

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

Simplifying both sides.

Subtracting x², 10x and 36 from both sides.

Dividing both sides by 2.

Letting x = 7 for the length of the hypotenuse.

step-by-step :