Question

joey is building a frame for a sandbox. the sandbox is going to be a quadrilateral that has the lengths shown. if the diagonal of the sandbox measures 14 feet, which best describes the shape of the sandbox? a rectangle, because angle c is a right angle a rectangle, because angle c and angle x are congruent a quadrilateral, because angle c and angle x are acute a quadrilateral, because angle c and angle x are obtuse

Explanation:

Step1: Check right triangle condition

Calculate sum of squares of sides: $8^2 + 12^2 = 64 + 144 = 208$
Calculate square of diagonal: $14^2 = 196$

Step2: Compare values for right angle

Since $8^2 + 12^2
eq 14^2$, angle C is not a right angle.

Step3: Classify angles

For angle C: the diagonal is shorter than the hypotenuse of a right triangle with legs 8 ft and 12 ft, so angle C is obtuse. By symmetry, angle X is also obtuse.

Answer:

a quadrilateral, because angle C and angle X are obtuse