Question

Sum of two positive square = 468. Find the number​

Answer 1

Step-by-step explanation:

Correct question :-

Sum of the areas of two squares is 468 m^2. If the difference of their perimeters is 24 m, find the sides of the two squares

To Find :-

Find the sides of the two squares

Solution :-

Area of the second square = (Y)²

According to question, (X)² + (Y)² = 468 m² ——(1).

Perimeter of first square = 4 × X and Perimeter of second square = 4 × Y

According to question,

4X – 4Y = 24 ——–(2)

From equation (2) we get,

4X – 4Y = 24, 4(X-Y) = 24

X – Y = 24/4 , X – Y = 6

X = 6+Y ———(3)

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Putting the value of X in equation (1)

(X)² + (Y)² = 468, (6+Y)² + (Y)² = 468

(6)² + (Y)² + 2 × 6 × Y + (Y)² = 468

36 + Y² + 12Y + Y² = 468

2Y² + 12Y – 468 +36 = 0

2Y² + 12Y -432 = 0

2( Y² + 6Y – 216) = 0

Y² + 6Y – 216 = 0

Y² + 18Y – 12Y -216 = 0

Y(Y+18) – 12(Y+18) = 0 (Y+18) (Y-12) = 0

(Y+18) = 0 Or (Y-12) = 0 Y = -18 OR Y = 12

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Putting Y = 12 in EQUATION (3)

X = 6+Y = 6+12 = 18

Side of first square = X = 18 m

Side of second square = Y = 12 m.

Answer 2

To Find

• Find the sides of the two squares

Solution

• Area of the second square = (Y)²

According to question

(X)² + (Y)² = 468 m² ——(1).

• Perimeter of first square = 4 × X
• Perimeter of second square = 4 × Y

According to question,

4X – 4Y = 24 ——–(2)

From equation (2) we get,

$\tt \: 4X – 4Y = 24 \\ \\ \tt \: 4(X-Y) = 24\\ \\ \tt \:X – Y = \frac{24}{4} \\ \\ \tt \:X – Y = 6 \\ \\ \tt \:X = 6+Y ———(3) \\ \\ \tt \:solving \: for \: x \\ \tt \: (X)² + (Y)² = 468, (6+Y)² + (Y)² = 468\\ \tt \: (6)² + (Y)² + 2 × 6 × Y + (Y)² = 468\\ \tt \: 36 + Y² + 12Y + Y² = 468\\ \tt \: 2Y² + 12Y – 468 +36 = 0\\ \tt \: 2Y² + 12Y -432 = 0\\ \tt \: 2( Y² + 6Y – 216) = 0\\ \tt \: Y² + 6Y – 216 = 0\\ \tt \: Y² + 18Y – 12Y -216 = 0\\ \tt \: Y(Y+18) – 12(Y+18) = 0 \\ \tt \: (Y+18) (Y-12) = 0 \\ \tt \: (Y+18) = 0 \\ \tt \: Or \: (Y-12) = 0 \\ \tt \: Y = -18 \: or \: Y = 12$

Putting Y = 12 in Eq (3)

X = 6+Y

= 6+12

= 18

• Side of first square = X = 18 m
• Side of second square = Y = 12 m.

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