Question

HELP PLS
If sides BD and DC have the same length, what is the length of side BC?
A. 1 unit
B. Square root 2 units
C. 2 units
D. Square root 3 units
E. 4 units

Answer 1

Answer:

  C.  2 units

Step-by-step explanation:

The ratio of side lengths in an isosceles right triangle is ...

   1 : 1 : √2

If you don't already have this memorized, you can figure it out using the Pythagorean theorem:

  BD² = AD² +AB² = 1 + 1 = 2

  BD = √2 . . . . taking the square root

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We are told that BD = DC, so we know the larger triangle is also an isosceles right triangle. This one has short sides of length √2, so the long side (BC) will have length (√2)×(√2) = 2.

The length of BC is 2 units.