Please help....
The figure is not drawn to scale. It shows two squares. the total area of two squares is 65 sq cm. the length of the smaller square is more that half the length of the larger square. given that the length of each square is a whole number, find the length of each square.
I did this for you
Always check back before reposting the same question.
a = the length of the larger square
b = the length of the smaller square
a ^ 2 + b ^ 2 = 65
Possible combinations :
a = 1 , b = 8 , a ^ 2 + b ^ 1 = 1 ^ 2 + 8 ^ 2 = 1 + 64 = 65
But the length of the smaller square is greater of the length of the larger square.
You must reject this solution.
a = 4 , b = 7 , a ^ 2 + b ^ 1 = 4 ^ 2 + 7 ^ 2 = 16 + 49 = 65
But the length of the smaller square is greater of the length of the larger square.
You must reject this solution.
a = 7 , b = 4 , a ^ 2 + b ^ 1 = 7 ^ 2 + 4 ^ 2 = 49 + 16 = 65
This is correct solution.
The length of the smaller square is more that half the length of the larger square.
4 > 7 / 2
4 > 3.5
a = 8 , b = 1 , a ^ 2 + b ^ 1 = 8 ^ 2 + 1 ^ 2 = 64 + 1 = 65
But the length of the smaller square is less that half the length of the larger square.
You must reject this solution.
Solution :
a = 7 cm , b = 4 cm
To find the length of each square, let's assume the length of the larger square is x cm.
According to the problem, the length of the smaller square is more than half the length of the larger square. So, the length of the smaller square can be represented as (x/2) + 1 (since we're told that the length is a whole number).
The area of a square is given by the formula: area = side^2.
So, the area of the larger square is x^2 cm^2, and the area of the smaller square is ((x/2) + 1)^2 cm^2.
According to the problem, the total area of the two squares is 65 cm^2:
x^2 + ((x/2) + 1)^2 = 65
Expanding and simplifying the equation:
x^2 + (x^2/4) + x + 1 = 65
Multiplying the entire equation by 4 to get rid of the fraction:
4x^2 + x^2 + 4x + 4 = 260
Combining like terms:
5x^2 + 4x + 4 = 260
Rearranging the equation:
5x^2 + 4x - 256 = 0
To solve this quadratic equation, you can use factoring, the quadratic formula, or completing the square. Factoring this equation may not be straightforward, so let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values:
x = (-(4) ± √((4)^2 - 4(5)(-256))) / (2(5))
Simplifying:
x = (-4 ± √(16 + 5120)) / (10)
x = (-4 ± √5136) / 10
x ≈ (-4 ± 71.66) / 10
x ≈ (-4 + 71.66) / 10 OR x ≈ (-4 - 71.66) / 10
Now, we have two possible values for x:
x ≈ 67.66 / 10 OR x ≈ -75.66 / 10
Since the length cannot be negative, we will consider only the positive value.
x ≈ 6.77
Now we know the length of the larger square is approximately 6.77 cm.
To find the length of the smaller square, we can substitute this value back into the equation we derived earlier:
Length of smaller square = (6.77/2) + 1
Length of smaller square ≈ 3.385 + 1
Length of smaller square ≈ 4.385
Since the length is required to be a whole number, we round up to the nearest whole number:
Length of smaller square ≈ 5 cm
Thus, the length of the larger square is approximately 6.77 cm, and the length of the smaller square is 5 cm.