35.
Sum of the areas of two squares is 544 m2. If the difference of their
perimeters is 32 m, find the sides of the two squares.
Answers
Side of the square is 12 m and 20 m.
Given:
- The sum of the areas of two squares is 544 sq.m.
- Difference between their perimeters is 32 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,
x² + y² = 544 ..................1
4x - 4y = 32 ......................2
4(x-y) = 32
Dividing "4" on both the sides, we get
x -y = 8
x = y + 8
From equation 1,
(Y + 8)² + Y² = 544
Y² + 64 + 16y + Y² = 544
2Y² + 16Y - 480 = 0
y² + 8y - 240 = 0
y² + 20y - 12y - 240 = 0
y(y + 20) - 12(y + 20) = 0
(y + 20)(y - 12) = 0
y = 12m
From equation 2,
x = y + 8
x = 12 + 8
x = 20m
Therefore, the side of the square is 12 m and 20 m.
To learn more....
1. Sum of the areas of two squares is 468 m square if the difference of their perimeter is 24 m find the sides of the two square
brainly.in/question/2163623
2. Sum of areas of two squares is 400 cm 2 .If the difference in their perimeters is 16cm. find the sides of the two squares
brainly.in/question/289826
Answer:
Let the sides of first and second square be X and Y .
Area of first square = (X)²
And,
Area of second square = (Y)²
According to question,
(X)² + (Y)² = 544 m² ------------(1).
Perimeter of first square = 4 × X
and,
Perimeter of second square = 4 × Y
According to question,
4X - 4Y = 32 -----------(2)
From equation (2) we get,
4X - 4Y = 32
4(X-Y) = 32
X - Y = 32/4
X - Y = 8
X = 8+Y ---------(3)
Putting the value of X in equation (1)
(X)² + (Y)² = 544
(8+Y)² + (Y)² = 544
(8)² + (Y)² + 2 × 8 × Y + (Y)² = 544
64 + Y² + 16Y + Y² = 544
2Y² + 16Y - 544 +64 = 0
2Y² + 16Y -480 = 0
2( Y² + 8Y - 240) = 0
Y² + 8Y - 240 = 0
Y² + 20Y - 12Y -240 = 0
Y(Y+20) - 12(Y+20) = 0
(Y+20) (Y-12) = 0
(Y+20) = 0 Or (Y-12) = 0
Y = -20 OR Y = 12
Putting Y = 12 in EQUATION (3)
X = 8+Y = 8+12 = 20
Side of first square = X = 20 m
and,
Side of second square = Y = 12 m.