Equation of diagonals of a rectangle with area 32 sq. units are y+2 x-4=0 and y-2 x-12= 0 , then equation(s) of its sides(s) is/are

Question

Equation of diagonals of a rectangle with area 32 sq. units are y+2 x-4=0 and y-2 x-12= 0 , then equation(s) of its sides(s) is/are (A) x =0 (B) y=10 (C) x=-4 (D) y=12

Tardigrade Admin · Accepted Answer

y + 2x - 4 = 0 y-2 x-12=0 y=8 ⇒ point of intersection of diagonals is (-2,8) x =-2 m 1+ m 2=-2+2=0 angle bisectors are parallel to x-axis y-axis. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/3034f49a25a35f5a69eea1cc59c902ac-.png" /> tan θ=(b/a)=2 ⇒ b=2 a text also 4 a b=32 8 a2=32 ⇒ a=2, b=4 ∴ text Equation of sides are x=0, x=-4, y=4, y=12

Q. Equation of diagonals of a rectangle with area $32 s q$ . units are $y + 2 x - 4 = 0$ and $y - 2 x - 12 =$ 0 , then equation(s) of its sides(s) is/are

$x = 0$

$y = 10$

$x = - 4$

$y = 12$

Q. Equation of diagonals of a rectangle with area 32sq. units are y+2x−4=0 and y−2x−12= 0 , then equation(s) of its sides(s) is/are

x=0

y=10

x=−4

y=12

y+2x−4=0 y−2x−12=0 y=8⇒ point of intersection of diagonals is (−2,8) x=−2 m1​+m2​=−2+2=0 angle bisectors are parallel to x-axis & y-axis. tanθ=ab​=2⇒b=2a also 4ab=32 8a2=32 ⇒a=2,b=4 ∴ Equation of sides are x=0,x=−4,y=4,y=12

Q. Equation of diagonals of a rectangle with area $32 s q$ . units are $y + 2 x - 4 = 0$ and $y - 2 x - 12 =$ 0 , then equation(s) of its sides(s) is/are

$x = 0$

$y = 10$

$x = - 4$

$y = 12$