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lora16 [44]
3 years ago
9

The area of a rectangle is 45 cm2. Two squares are constructed such that two adjacent sides of the rectangle are each also the s

ide of one of the squares. The combined area of the two squares is 106 cm². Find the lengths of the sides of the squares.
Mathematics
2 answers:
Zielflug [23.3K]3 years ago
6 0

Answer:

The lengths of sides of squares are 5 cm and 9 cm.

Step-by-step explanation:

Let the sides of rectangle be x and y .

Area of rectangle = Length × Breadth

Given : Area of rectangle = 45 cm².

⇒ x × y  = 45  

⇒ x=\frac{45}{y}  ........(1)

Two squares are constructed such that two adjacent sides of the rectangle

so squares have side x and y .

Area of square = side × side

Area of square with side x = x²

Area of square with side y = y²

Also, The combined area of the two squares is 106 cm².

⇒ x² + y² = 106

From (1) put value of x , we get,

(\frac{45}{y})^2+y^2=106

Solving for y ,

(\frac{45}{y})^2+y^2=106  

2025+y^4=106y^2  

y^4-106y^2+2025=0  

y^4-81y^2-25y^2+2025=0  

y^2(y^2-81)-25(y^2-81)=0  

(y^2-25)(y^2-81)=0

y^2-81=0 or y^2-25=0    

on solving we get y = 5 and y = 9

Also, x can be find by putting in (1),

⇒ x=\frac{45}{5}=9 and ⇒ x=\frac{45}{9}=5  

⇒ x = 9 and x = 5

Thus, lengths of sides of squares are 5 cm and 9 cm.

Aleksandr [31]3 years ago
6 0

Answer: 5 cm and 9 cm


Step-by-step explanation:

If the two squares are x and y, then

xy = 45

x^2 + y^2 = 106

so,

x^2 + (45/x)^2 = 106

x^2 + 2025/x^2 = 106

x^4 - 106x^2 + 2025 = 0

(x^2-25)(x^2-81) = 0

x^2 = 25 and 81

x = 5 and 9

yep, 5*9 = 45

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Exercise (a)

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