The ratio of the diagonals of a kite is 3:4. If the area of the kite is 150, find the longer diagonal?

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The ratio of the diagonals of a kite is 3:4. If the area of the kite is 150, find the longer diagonal?

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Answer 1 · 2018-06-24T14:10:51

$longer diagonal = 10 \sqrt{2}$ $"longer diagonal "=10sqrt2$

Explanation:

$the area (A) of a kite is the product of the diagonals$ $"the area (A) of a kite is the product of the diagonals"$

$∙ x A = d_{1} d_{2}$ $•color(white)(x)A=d_1d_2$

$where d_{1} and d_{2} are the diagonals$ $"where "d_1" and "d_2" are the diagonals"$

$given \frac{d_{1}}{d_{2}} = \frac{3}{4} then$ $"given "d_1/d_2=3/4" then"$

$d_{2} = \frac{4}{3} d_{1} \leftarrow d_{2} is the longer diagonal$ $d_2=4/3d_1larrd_2color(blue)" is the longer diagonal"$

$forming an equation$ $"forming an equation"$

$d_{1} d_{2} = 150$ $d_1d_2=150$

$d_{1} \times \frac{4}{3} d_{1} = 150$ $d_1xx4/3d_1=150$

$d_{1}^{2} = \frac{450}{4}$ $d_1^2=450/4$

$d_{1} = \sqrt{\frac{450}{4}} = \frac{15 \sqrt{2}}{2}$ $d_1=sqrt(450/4)=(15sqrt2)/2$

$\Rightarrow d_{2} = \frac{4}{3} \times \frac{15 \sqrt{2}}{2} = 10 \sqrt{2}$ $rArrd_2=4/3xx(15sqrt2)/2=10sqrt2$

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The ratio of the diagonals of a kite is 3:4. If the area of the kite is 150, find the longer diagonal?

1 Answer

Explanation:

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