Question

Sum of the areas of two squares is 544 m square if the difference of their perimeter is 32m find the sides of the two square

Answer 1

Answer:

Let the sides of first and second square be X and Y .

Area of first square = (X)²

And,

Area of second square = (Y)²

According to question,

(X)² + (Y)² = 544 m² ------------(1).

Perimeter of first square = 4 × X

and,

Perimeter of second square = 4 × Y

According to question,

4X - 4Y = 32 -----------(2)

From equation (2) we get,

4X - 4Y = 32

4(X-Y) = 32

X - Y = 32/4

X - Y = 8

X = 8+Y ---------(3)

Putting the value of X in equation (1)

(X)² + (Y)² = 544

(8+Y)² + (Y)² = 544

(8)² + (Y)² + 2 × 8 × Y + (Y)² = 544

64 + Y² + 16Y + Y² = 544

2Y² + 16Y - 544 +64 = 0

2Y² + 16Y -480 = 0

2( Y² + 8Y - 240) = 0

Y² + 8Y - 240 = 0

Y² + 20Y - 12Y -240 = 0

Y(Y+20) - 12(Y+20) = 0

(Y+20) (Y-12) = 0

(Y+20) = 0 Or (Y-12) = 0

Y = -20 OR Y = 12

Putting Y = 12 in EQUATION (3)

X = 8+Y = 8+12 = 20

Side of first square = X = 20 m

and,

Side of second square = Y = 12 m.

Answer 2

Step-by-step explanation:

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