Question

the sum of the areas of two squares is 400sq.m if the difference between their perimeters is 16 m , find the sides of two squares
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Answer 1

Answer:

Let the side of first square=x

Side of second square=y

4x-4y=16m

X-Y=4

X=Y+4. __________(1)

(X)²+(Y)²=400m²

From (1)

(Y+4)²+Y2=400

Y²+16+8y+Y²=400

2Y²+8Y-384=0

y²+4y-192=0

y²+16y-12y-192=0

y(y+16)-12(y+16)=0

(y+16)(y-12)=0

y=12m.

X=y+4

X=12+4=16m.

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Step-by-step explanation:

Answer 2

Side of the square is 12 m and 16 m.

Given:

• The sum of the areas of two squares is 400 sq.m.
• Difference between their perimeters is 16 m.

To find:

The sides of two squares.

Formula used:

• Area of square = (side)²
• Perimeter of square = 4 × side

Explanation:

Let us consider,

Side of first square = x

Side of second square = y

From given data,

The sum of the areas of two squares is 400 sq.m :        

x² + y² = 400 .......................1        

Difference between their perimeters is 16 m :

4x - 4y = 16              

4(x-y) = 16        

Dividing "4" on both the sides, we get    

x - y  = 4       .........................2                

x = 4+y    

From equation 1,    

(Y+4)² + Y² = 400        

Y² + 16 + 8y + Y² = 400        

2Y² + 8Y - 384 = 0            

y² + 4y - 192 = 0    

y² + 16y - 12y - 192 = 0  

y(y + 16) -12(y + 16) = 0          

(y + 16)(y - 12) = 0                  

y = 12m.

From equation 2,  

x = 4 + y

x = 4 + 12

x = 16m.

Therefore, the side of the square is 12 m and 16 m.

To learn more....

Importance of mensuration

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