Question

HELP! Please pyth. theorem

Answer 1

Given:

The given triangle QPO is a right triangle.

The length of QP is 5 units.

The length of OP is (x + 5) units.

The length of QO is (x + 6) units.

We need to determine the hypotenuse of the triangle QPO.

Value of x:

The value of x can be determined using the Pythagorean theorem.

Thus, we have;

$QO^2=QP^2+OP^2$

Substituting the values, we get;

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

Expanding, we get;

$x^2+12x+36=25+x^2+10x+25$

Adding the like terms, we get;

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

       $12x+36=10x+50$

         $2x+36=50$

                 $2x=14$

                   $x=7$

Thus, the value of x is 7.

Length of the hypotenuse:

The hypotenuse of the triangle QPO is QO.

Substituting x = 7 in the length of QO, we get;

$QO=7+6$

$QO=13$

Thus, the length of the hypotenuse is 13 units.

Hence, Option D is the correct answer.