The area of the rhombus ABCD is 24. The equation of the diagonal BD is 4x + 3y + 2 = 0 and A = (3, 2). The length of the side of the rhombus is ______.

Question

The area of the rhombus $A B C D$ is 24. The equation of the diagonal BD is $4 x + 3 y + 2 = 0$ and $A = (3, 2)$ . The length of the side of the rhombus is ______.

Smart Achievers · Accepted Answer

(5)

$Let A C and B D intersect at P .$

$Now, A P = \frac{12 + 6 + 2}{\sqrt{16 + 9}} = 4$

$∴$ $Area of ∆ A B D = A P \times B P = \frac{24}{2} = 12$ $\Rightarrow B P = 3$

$∴$ $A B = \sqrt{A P^{2} + B P^{2}} = 5$

Solution

Q.
The area of the rhombus $A B C D$ is 24. The equation of the diagonal BD is $4 x + 3 y + 2 = 0$ and $A = (3, 2)$ . The length of the side of the rhombus is ______.

Ans.
(5)

$Let A C and B D intersect at P .$

$Now, A P = \frac{12 + 6 + 2}{\sqrt{16 + 9}} = 4$

$∴$ $Area of ∆ A B D = A P \times B P = \frac{24}{2} = 12$ $\Rightarrow B P = 3$

$∴$ $A B = \sqrt{A P^{2} + B P^{2}} = 5$

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Solution

Q. The area of the rhombus ABCD is 24. The equation of the diagonal BD is 4x+3y+2=0 and A=(3, 2). The length of the side of the rhombus is ______.

Ans. (5) Let AC and BD intersect at P. Now, AP=12+6+216+9=4 ∴ Area of ∆ABD=AP×BP=242=12⇒BP=3 ∴ AB=AP2+BP2=5

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Q.
The area of the rhombus $A B C D$ is 24. The equation of the diagonal BD is $4 x + 3 y + 2 = 0$ and $A = (3, 2)$ . The length of the side of the rhombus is ______.

Ans.
(5)

$Let A C and B D intersect at P .$

$Now, A P = \frac{12 + 6 + 2}{\sqrt{16 + 9}} = 4$

$∴$ $Area of ∆ A B D = A P \times B P = \frac{24}{2} = 12$ $\Rightarrow B P = 3$

$∴$ $A B = \sqrt{A P^{2} + B P^{2}} = 5$