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Tanya [424]
3 years ago
15

The length of each side of a square is 3 inches more than the length of each side of a small square. The sum of the areas of the

square is 549 inches. Find the lengths of the sides of the two squares.
Mathematics
1 answer:
NeX [460]3 years ago
7 0

Answer:

\text{Smaller square's 15 inches, Bigger square's 18 inches}

Step-by-step explanation:

GIVEN: The length of each side of a square is 3 inches more than the length of each side of a small square. The sum of the areas of the square is 549 inches.

TO FIND: the lengths of the sides of the two squares.

SOLUTION:

let the length of side of small square be \text{x}

Area of small square =(\text{side})^2=\text{x}^2

As length of each side of bigger square is 3\text{ inches} more than the smaller square

length of side of bigger square =\text{x}+3\text{ inches}

Area of bigger square =(\text{x+3})^2

Also

Sum of areas of both square =549\text{ inch}^2

(\text{x})^2+(\text{x+3})^2=549

2\text{x}^2+6\text{x}+9=549

\text{x}^2+3\text{x}-270=0

\text{x}=15,-18

as the length of side can never be negative

\text{x}=15

length of side of smaller square =15\text{ inches}

length of side of bigger square =\text{x}+3\text{ inches}=18\text{ inches}

Hence the length of smaller and bigger square are 15\text{ inches} and 18\text{ inches} respectively.

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