Question

The perimeter of a square exceeds that of another by 100 feet and the area of the bigger square exceeds three times the area of a smaller square by 325 sq. Ft find the length of each side of the two squares

Answer 1

Given :-

• The perimeter of a square exceeds that of another by 100 feet and the area of the bigger square exceeds three times the area of a smaller square by 325 sq. Ft

To find :-

• Length of each side of the two squares

Solution :-

Let the side of the small square be x then side of the big square be y

As we know that

Perimeter of square = 4 × side

Area of square = side × side

According to the question

• Perimeter of a square exceeds that of another by 100 feet

→ 4y = 4x + 100

→ 4y - 4x = 100

→ 4(y - x) = 100

→ y - x = 25

→ y = 25 + x ----(i)

• Area of the bigger square exceeds three times the area of a smaller square by 325 sq. Ft

→ y² = 3x² + 325

Now substitute the value of y

→ (x + 25)² = 3x² + 325

→ x² + 50x + 625 = 3x² + 325

→ 2x² - 50x - 300 = 0

→ x² - 25x - 150 = 0

Split middle term

→ x² - 30x + 5x - 150 = 0

→ x(x - 30) + 5(x - 30) = 0

→ (x - 30) (x+5) = 0

Hence,

x = 30 or x = -5

★ A length cannot be in negative ★

So x = 30

Put the value of x eqⁿ (i)

→ y = x + 25

→ y = 30 + 25

→ y = 55

Hence,

• Side of small square = x = 30 feet
• Side of big square = y = 55 feet