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. a rectangle, because angle C is a right angle

B. a rectangle, because angle C and angle X are congruent

C. a quadrilateral, because angle C and angle X are acute

D, a quadrilateral, because angle C and angle X are obtuse

Answer 1

we know that
applying the Pythagoras Theorem
c²=a²+b²
where
c=14 ft
a=8 ft
b=12 ft

case a)
if 
c²=a²+b²-------> C is a right angle 

case b) 
if 
c²< (a²+b²)-------> C is an acute angle 

case c) 
if 
c² > (a²+b²)-------> C is an obtuse angle 

c²=14²-----> 196
(a²+b²)=8²+12²-----> 208
196 < 208
c² < (a²+b²)------>  C is an acute angle 

therefore

the answer is the option
C. a quadrilateral, because angle C and angle X are acute

Answer 2

The shape of the sandbox is a quadrilateral because angle C and angle X are acute and this can be determined by using the Pythagorean theorem.

Given :

• The sandbox is going to be a quadrilateral that has the lengths shown.
• The diagonal of the sandbox measures 14 feet.

The Pythagorean theorem can be used in order to determine given angle X and angle C are obtuse or acute.

According to the Pythagorean theorem --

If the sum of the squared of the shorter side is greater than the square of the larger side then the angle is an acute angle, that is:

$c^2<a^2+b^2$

If the sum of the squared of the shorter side is less than the square of the larger side then the angle is an obtuse angle, that is:

$c^2>a^2+b^2$

If the sum of the squared of the shorter side is equal to the square of the larger side then the angle is a right angle.

$c^2=a^2+b^2$

Now, check the angle is obtuse, acute, or right by using the Pythagorean theorem.

$c^2=14^2=196$

$a^2+b^2=8^2+12^2=208$

208 > 196

So, angle X and angle C are acute angles. Therefore, the correct option is C).

For more information, refer to the link given below:

https://brainly.com/question/16426393