𝐴𝐵𝐶𝐷 is a kite where 𝐴𝐶 is equal to 23 inches and its area equals 115 square inches. Determine the length of 𝐵𝐷.
So we’ve been told the area of a kite and the length of one of its diagonals 𝐴𝐶. Our task is to calculate the length of the second diagonal. In order to do so, we need to recall the formula for calculating the area of a kite.
If a kite has diagonals 𝑑 one and 𝑑 two, then its area can be found by calculating half of their product. In this question, the two diagonals of the kite are the lines 𝐴𝐶 and 𝐵𝐷. And therefore, we have that the area is equal to one-half of the length of 𝐴𝐶 multiplied by the length of 𝐵𝐷.
Remember, we’ve been given the area and the length of 𝐴𝐶. Let’s substitute these values into the formula. We now have that 115 is equal to a half multiplied by 23 multiplied by 𝐵𝐷. In order to find the length of 𝐵𝐷, we need to solve this equation.
The first step is to eliminate the fraction on the right-hand side by multiplying both sides of the equation by two. This gives 230 is equal to 23 multiplied by 𝐵𝐷.
The final step to solve for 𝐵𝐷 is to divide both sides of the equation by 23. 230 divided by 23 is 10. And so we have that 10 is equal to 𝐵𝐷. Therefore, the length of 𝐵𝐷, which is the second diagonal of this kite, is 10 inches.