Question

If the shape is a true rectangle, can the value of x be 54?A. Yes, 36 + 18 = 54 so ADB and CDB must be right triangles.B. Yes, 362 + 182 = 54^2 so ADB and CDB must be right triangles.C. No, since 36 + 18 * 54 then ADB and CDB cannot be right triangles.D. No, since 36^2 +18^2 is not equal to 54^2 then ADB and CDB cannot be right triangles.

Answer 1

if the shape is a true rectangle, the triangles that the length and the width makes with the diagonal (ADB and CDB) are right triangles.Therefore, it must satisfy the Pythagorean Theorem.

`c^2=a^2+b^2`

when a = 36 and b = 18, c which is x must be 54 according to the probem, we can verify if that is true.

`\begin{gathered} c^2=a^2+b^2 \\ x^2=36^2+18^2 \\ x^2=1296+324 \\ x^2=1620 \\ x=40.25 \end{gathered}`

Thus, x is not equal to 54 but 40.25. Therefore, the answer is No, since 36^2 +18^2 is not equal to 54^2 then ADB and CDB cannot be right triangles.

Answer: D