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