Question

A rectangle is 12 cm long and 9 cm wide. Its diagonal is labeled 2x - 11. What is the value of x?

Answer 1

Answer: The value of x is 13 cm.

Explanation:

It is given that the length and width of the rectangle are 12 cm  and 9 cm.

Use pythagoras to find the value of the diagonal.

$Hypotenuse=\sqrt{(base)^2+(perpendicular)^2}$

$D=\sqrt{(12)^2+(9)^2}$

$D=\sqrt{144+81}$

$D=\sqrt{225}$

$D=15$

It is given that the diagonal is labeled as 2x-11.

$2x-11=15$

$2x=15+11$

$2x=26$

Divide both side by 2.

$x=13$

Therefore, x = 13cm.

Answer 2

Answer: 13

Step-by-step explanation:

Use Pythagorean Theorem to find the length of the diagonal (aka hypotenuse) which is also equal to 2x - 11.

12² + 9² = hypotenuse²

144 + 81 = hypotenuse²

144 + 81 = (2x - 11)²

    225 = (2x - 11)²

 √225 = √(2x - 11)²

     15   = 2x - 11

   +11           +11

     26  = 2x

     ÷2    ÷2  

      13  = x