# Flowerbed

Family cultivated tulips on a square flower bed of 6 meters. Later they added the square terrace with a side of 7 meters to their house. One vertex of the terrace lay exactly in the middle of a tulip bed, and one side of the terrace divided the side of the tulip bed in a ratio of 1: 5.
In what proportion did the other side of the terrace split the other side of the flower bed? How many square meters of terraces have their tulips shrunk?

Result

M = (Correct answer is: 1/5) S =  9 m2

#### Solution:

$M=1:5$
$a = 6 \ \\ b = a/2 = 6/2 = 3 \ \\ \ \\ A = b \cdot \ (b-1)/2 = 3 \cdot \ (3-1)/2 = 3 \ m^2 \ \\ B = b \cdot \ b = 3 \cdot \ 3 = 9 \ m^2 \ \\ S = B-A+A = 9-3+3 = 9 = 9 \ m^2$

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