A wire of length 50cm is cut into two parts and each part is bent to form a square. If the total area of the two square is 100cm², find the perimeter of each square.
let each side of one square be x cm
let the other have side length y cm
so we know:
x^2 + y^2 = 100 ***
and
4x + 4y = 50
2x+2y=25 **
y = (25-2x)/2
subbing the 2nd part into the first:
x^2 + (625 - 100x + 4x^2)/4 = 100
times 4
4x^2 + 625 - 100x + 4x^2 = 400
8x^2 - 100x + 225 = 0
by the formula, I got
x = appr 9.557
sub that into ** to get y, and go from there
To solve this problem, we need to follow these steps:
Step 1: Let's assume that one part of the wire is used to form side A of the square, and the other part is used to form side B of the square.
Step 2: We know that the total length of the wire is 50 cm. So, we can relate the length of side A and side B with the total length of the wire using the equation:
Length of side A + Length of side B = Total length of the wire.
Step 3: Since we have information about the area of both squares, let's write equations based on the area of each square:
Area of square A = side A * side A
Area of square B = side B * side B
Step 4: We know that the sum of the areas of both squares is 100 cm². So, we can write the equation:
Area of square A + Area of square B = 100 cm²
Step 5: Using equations from Steps 2 and 4, we can substitute the values and simplify:
(side A * side A) + (side B * side B) = 100 cm²
Step 6: Now, let's solve for side A in terms of side B using the equation from Step 2:
Length of side A = Total length of the wire - Length of side B
side A = 50 cm - side B
Step 7: Substitute side A from Step 6 into the equation from Step 5:
(side B * side B) + ((50 cm - side B) * (50 cm - side B)) = 100 cm²
Step 8: Simplify the equation using algebraic operations:
side B² + (50 cm - side B)² = 100 cm²
side B² + 2500 cm² - 100 cm * side B + side B² = 100 cm²
2 * side B² - 100 cm * side B + 2500 cm² - 100 cm² = 0
2 * side B² - 100 cm * side B + 2400 cm² = 0
Step 9: Solve the equation using the quadratic formula or factoring. The equation is in the form of ax² + bx + c = 0, where:
a = 2, b = -100 cm, and c = 2400 cm²
Step 10: Using the quadratic formula or factoring, we can find the two possible values of side B.
Step 11: Since we are looking for the perimeter of the square (4 * side), we can use the values of side B to calculate the perimeter of each square.
Following these steps, you can find the perimeter of each square.