The sum of the areas of two square is 41q cm. If the sum of their perimeter is 36 cm then find the side of two square
Answers
Given,
- The sum of the areas of two square is 41cm².
- The sum of their perimeter is 36 cm.
To Find,
- Find the side of two square.
Solution,
Let's
The Side Of First Square = X
The Side Of Second Square = Y
The Area Of First Square
→ (Side)²
→ X²
The Area Of Second Square
→ (Side)²
→ Y²
The Perimeter of First Square
→ 4(Side)
→ 4(X)
→ 4X
The Perimeter of Second Square
→ 4(Side)
→ 4(Y)
→ 4Y
Sum of The Areas = 41cm²
→ X² + Y² = 41cm²
Sum of the Perimeters = 36cm
→ 4X + 4Y = 36cm
→ 4(X + Y) = 36cm
→ X + Y = 9cm
X² + Y² = 41 •••(1st)
X + Y = 9 •••(2nd)
Finding The Value of Y in 2nd Equation;
X + Y = 9 •••(2nd)
Y = 9 - X •••(3rd)
Substituting the Value Of Y in 1st Equation;
X² + Y² = 41 •••(1st)
→ X² + (9 - X)² = 41
→ X² + 81 - 2(9)(X) + X² = 41
→ X² + X² + 81 - 41 - 18X = 0
→ 2X² - 18X + 40 = 0
→ 2(X² - 9X + 20) = 0
→ X² - 9X + 20 = 0/2
→ X² - 9X + 20 = 0
→ X² - 5X - 4X + 20 = 0
→ X(X - 5) - 4(X - 20) = 0
→ (X - 4)(X - 5) = 0
X - 4 = 0
X = 4
Substituting the Value Of X in 2nd Equation;
Y = 9 - X •••(3rd)
Y = 9 - X
Y = 5
Required Answer,
Sides Are 4cm And 5cm.