Answer:
- Length of diagonal 1: 8 meters
- Length of diagonal 2: 10 meters
Step-by-step explanation:
Let d1 be the first diagonal and d2 be the second diagonal.
Given
Area = 40 square meters
And one diagonal is 2 meter longer than other
[tex]d_2 = d_1+2[/tex]
The formula for area of kite is;
[tex]Area = \frac{1}{2} * d_1 * d_2[/tex]
Putting the known values
[tex]40 = \frac{1}{2} * d_1 * (d_1+2)\\80 = (d_1)^2+2d_1\\d_1^2 +2d_1-80 = 0\\[/tex]
The expression is a quadratic polynomial
Factorizing
[tex]d_1^2 + 10d_1-8d_1-80 = 0\\d_1(d_1+10)-8(d_1+10) = 0\\(d_1+10)(d_1-8) = 0\\d_1 + 10 = 0\\d_1 = -10\\d_1-8 = 0\\d_1 = 8[/tex]
As the value of length cannot be negative so discarding the negative value
[tex]d_1 = 8d_2 = d_1+2 = 8+2 =10[/tex]
Hence,
- Length of diagonal 1: 8 meters
- Length of diagonal 2: 10 meters
