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# One square has a side of 3 meters shorter than the side of a second square. the area of the longer square is 4 times, the area of the smaller square. find the length of a side of each square.

• Réponse publiée par: snow01
Smaller square has a side of 3 meters while the bigger square has a side of 6 meters.

Step-by-step explanation:

Side (s)  of second, bigger square: x

Side of shorter square: x-3 (shorter by 3 meters than the second square)

Area = s²  where s is the side

Area of smaller square = (x-3)²  (where x is the side)

Area of bigger, second square = x²

Condition:

The area of the bigger square is 4 times the area of the smaller square.

Equation:

x² = 4(x-3)²

x²  = 4(x² - 6x + 9)

x² = 4x² - 24x + 36

4x² - x² - 24x + 36 = 0

3x² - 24x + 36 = 0

3(x² - 8x + 12) = 0

Factor (x² - 8x + 12) then equate each factor to 0:

(x - 2) (x - 6) = 0

x-2= 0

x = 2

x - 6 = 0

x = 6

Choose the higher value from where 3 meter will be subtracted: x = 6

Substitute x = 6 to find the length of each side:

Second, bigger square: x = 6 meters

Smaller square: x-3 = 6-3 = 3 meters

Smaller square has a side of 3 meters while the bigger square has a side of 6 meters.

Check:

Area of smaller square = (3 meters)² = 9 meters²

Area of bigger square = (6 meters)² = 36 meters²

Condition:

The area of the bigger square is 4 times the area of the smaller square.

36 = 4(9)

36 = 36  (True)

• Réponse publiée par: cyrishlayno