Question Video: Finding the Diagonal Length of a Kite given Its Area and the Other Diagonal Length | Nagwa Question Video: Finding the Diagonal Length of a Kite given Its Area and the Other Diagonal Length | Nagwa

# Question Video: Finding the Diagonal Length of a Kite given Its Area and the Other Diagonal Length

π΄π΅πΆπ· is a kite where π΄πΆ = 23 in and its area equals 115 inΒ². Determine the length of π΅π·.

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### Video Transcript

π΄π΅πΆπ· is a kite where π΄πΆ is equal to 23 inches and its area equals 115 square inches. Determine the length of π΅π·.

So weβve been told the area of a kite and the length of one of its diagonals π΄πΆ. 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 π one and π 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 π΄πΆ and π΅π·. And therefore, we have that the area is equal to one-half of the length of π΄πΆ multiplied by the length of π΅π·.

Remember, weβve been given the area and the length of π΄πΆ. Letβs substitute these values into the formula. We now have that 115 is equal to a half multiplied by 23 multiplied by π΅π·. In order to find the length of π΅π·, 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 π΅π·.

The final step to solve for π΅π· 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 π΅π·. Therefore, the length of π΅π·, which is the second diagonal of this kite, is 10 inches.

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