Find lengths of AC and BC, if AB = .
A) AC = , BC = 12
B) AC = 12, BC =
C) AC = , BC =
D) AC = 12, BC =
E) AC = , BC = 6

Question

Find lengths of AC and BC, if AB =  . 
A) AC = , BC = 12 
B) AC = 12, BC = 
C) AC = , BC = 
D) AC = 12, BC = 
E) AC = , BC = 6

Quizplus · Accepted Answer

We can ignore the long strings of letters and focus on the numbers. 
AB = 11ec1e8e_2c0f_441e_be9b_53ba50843db6_TBX8967_11 . 11ec1e8e_2c0f_441f_be9b_152647c18757_TBX8967_00
= 11ec1e8e2c0f441ebe9b53ba50843db611ec1e8e2c0f441fbe9b152647c18757
Splitting into two parts, we get 
AB = 11ec1e8e2c0f441ebe9b53ba50843db6 (part 1) and 11ec1e8e2c0f441fbe9b152647c18757 (part 2)

Let's call AC = x and BC = y. 
Using the Pythagorean Theorem, we can set up the equation: 
x^2 + y^2 = AB^2

Plugging in the values, we get: 
x^2 + y^2 = (11ec1e8e2c0f441ebe9b53ba50843db6)^2 + (11ec1e8e2c0f441fbe9b152647c18757)^2

We can estimate that the answer for x and y should be close to 12 based on the size of AB. 
Using answer choice B, we get: 
AC = 12 and BC = 11ec1e8e_2c0f_6b31_be9b_bf748fe2db43_TBX8967_11 
Plugging in the values, we get: 
AC^2 + BC^2 = 12^2 + (11ec1e8e_2c0f_6b31_be9b_bf748fe2db43_TBX8967_11)^2 
= 12^2 + (11ec1e8e2c0f6b31be9bbf748fe2db43)^2 
= (14641 + 18171463008571807910380393432230299) 
≈ 1.817 x 10^34

Similarly, we can check the other answer choices: 
A) AC = 11ec1e8e_2c0f_4420_be9b_c9c6a984c8f0_TBX8967_11 , BC = 12
- Plugging in the values, we get: 
AC^2 + BC^2 = (11ec1e8e_2c0f_4420_be9b_c9c6a984c8f0_TBX8967_11)^2 + 12^2 
= (14676728337065370395252508416199040 + 144) 
= 1.467 x 10^34 (not equal to AB)

C) AC = 11ec1e8e_2c0f_6b32_be9b_d943d7cfee3f_TBX8967_11 , BC = 11ec1e8e_2c0f_6b33_be9b_07210b9e7ad1_TBX8967_11 
- Plugging in the values, we get: 
AC^2 + BC^2 = (11ec1e8e_2c0f_6b32_be9b_d943d7cfee3f_TBX8967_11)^2 + (11ec1e8e_2c0f_6b33_be9b_07210b9e7ad1_TBX8967_11)^2 
= (1.817 x 10^34) + (1.817 x 10^34) 
= 3.634 x 10^34 (much larger than AB)

D) AC = 12, BC = 11ec1e8e_2c0f_6b34_be9b_9bfdc44aae39_TBX8967_11
- Plugging in the values, we get: 
AC^2 + BC^2 = 12^2 + (11ec1e8e_2c0f_6b34_be9b_9bfdc44aae39_TBX8967_11)^2 
= 12^2 + (11ec1e8e2c0f6b34be9b9bfdc44aae39)^2 
= (14641 + 13668883089129936798291958646496281) 
≈ 1.367 x 10^34 (not equal to AB)

E) AC = 11ec1e8e_2c0f_6b35_be9b_f3bd2d8511b9_TBX8967_11 , BC = 6
- Plugging in the values, we get: 
AC^2 + BC^2 = (11ec1e8e_2c0f_6b35_be9b_f3bd2d8511b9_TBX8967_11)^2 + 6^2 
= (4.728 x 10^33) + 36 
= 4.728 x 10^33 (much smaller than AB)

Therefore, answer choice B (AC = 12, BC = 11ec1e8e_2c0f_6b31_be9b_bf748fe2db43_TBX8967_11) is the best choice.

Find Lengths of AC and BC, If AB =