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vazorg [7]
3 years ago
10

What is the length of line PS

Mathematics
1 answer:
stiks02 [169]3 years ago
4 0
PQ^2 = PR \times PS

(4x + 4)^2 = (3x + 3)(3x + 3 + 21)

16x^2 + 32x + 16= (3x + 3)(3x + 24)

16x^2 + 32x + 16= 9x^2 + 81x + 72

7x^2 - 49x- 56 = 0

7(x^2 - 7x - 8)= 0

(x - 8)(x + 1) = 0

x - 8 = 0~~~or~~~x + 1 = 0

x = 8~~~or~~~x = -1

x = -1 makes the lengths of segments PQ and PR equal zero.
That is not possible, so the solution x = -1 is discarded.

x = 8

PS = 3x + 3 + 21

PS = 3x + 24

PS = 3(8) + 24

PS = 24 + 24

PS = 48
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