2. If PQ = 21 cm and QR = 5 cm, then what are the possible lengths for PR so that can form a triangle? Explain your reasoning.
1 answer:
Check the picture below.
now, notice the first, black, triangle, so PR is some length that in order to make a triangle, needs to touch at P.
in the first case, the red triangle, if we stretch the angle at Q that much, PR is "almost" getting to be 5 + 21 in length, or 26, however, if it ever becomes 26, it'll be just pancaked against the other two lines and there's no triangle, just a flat thicker line, so it can't be 26, it has to be less than that.
in the second case, the green triangle, we shrink the angle at Q, if we shrink it so much, "almost" to flat-line with QP what would happen is what's leftover from the tip of QR to PR is 21 - 5, or 16 units, so PR could be 16 in that case however, if that ever happens, well, we again don't have a triangle, since the angle at Q would had shrunk to 0° and made a thick flat-line instead of a triangle, so PR can't be 16 either.
so PR cannot be 26, or we get a flat-line, and it cannot be 16 either, or we again get a flat-line, so it has to be 16 < PR < 26.
now, notice the first, black, triangle, so PR is some length that in order to make a triangle, needs to touch at P.
in the first case, the red triangle, if we stretch the angle at Q that much, PR is "almost" getting to be 5 + 21 in length, or 26, however, if it ever becomes 26, it'll be just pancaked against the other two lines and there's no triangle, just a flat thicker line, so it can't be 26, it has to be less than that.
in the second case, the green triangle, we shrink the angle at Q, if we shrink it so much, "almost" to flat-line with QP what would happen is what's leftover from the tip of QR to PR is 21 - 5, or 16 units, so PR could be 16 in that case however, if that ever happens, well, we again don't have a triangle, since the angle at Q would had shrunk to 0° and made a thick flat-line instead of a triangle, so PR can't be 16 either.
so PR cannot be 26, or we get a flat-line, and it cannot be 16 either, or we again get a flat-line, so it has to be 16 < PR < 26.
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