In a kite, the diagonals intersect at right angles and bisect each other. Let's denote the length of diagonal AG as d1 and the length of diagonal EM as d2. Then, the area of the kite can be expressed as:
Area of kite = (d1 x d2) / 2
Since the diagonals of the kite bisect each other, we know that AG = GM and AE = EM = 10 cm (since opposite sides of a kite are equal in length). Therefore, we can rewrite the area of the kite as:
Area of kite = (AG x AE) / 2
Substituting the given values, we get:
65 cm² = (AG x 10 cm) / 2
Multiplying both sides by 2, we get:
130 cm² = AG x 10 cm
Dividing both sides by 10 cm, we get:
AG = 13 cm
Therefore, the length of GM is also 13 cm (since AG = GM).
Answers & Comments
Answered by GenuisPanda
March 14, 2023
ORIGINAL
Answer:
In a kite, the diagonals intersect at right angles and bisect each other. Let's denote the length of diagonal AG as d1 and the length of diagonal EM as d2. Then, the area of the kite can be expressed as:
Since the diagonals of the kite bisect each other, we know that AG = GM and AE = EM = 10 cm (since opposite sides of a kite are equal in length). Therefore, we can rewrite the area of the kite as:
Substituting the given values, we get:
Multiplying both sides by 2, we get:
Dividing both sides by 10 cm, we get:
Therefore, the length of GM is also 13 cm (since AG = GM).