Question

10. In a quadrilateral ABCD, verify that AB + BC + CD+DA+ AC + BD.​

Answer 1

Answer:

this is the correct answer

Answer 2

Now visually identify that the quadrilateral ABCD. It is divided by diagonals AC and BD into four triangles

$\large{ \bold{ \star \: { \sf{given}}}}$

Now, take each triangle separately and apply the above property and then add LHS and RHS of the equation formed.

In triangle ABC,

AB + BC > AC (1)

In triangle ADC,

AD + CD > AC (2)

In triangle ADB,

AD + AB > DB (3)

In triangle DCB,

DC+ CB > DB. . _______.(4)

Adding equation (1), (2), (3) and (4) we get,

AB + BC + AD + CD + AD + AB + DC+ CB > AC + AC + DB + DB

AB + AB + BC + BC + CD + CD + AD + AD > 2AC + 2DB

2AB + 2BC + 2CD + 2AD > 2AC + 2DB

(Hence, AB + BC + CD + DA > AC + BD)

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$\large{ \sf{ \: \: formula \: for \: quadrilaterals}}$

$\large{ \red {area \: of \: rectangle = l \times b}}$

$\large{ \orange{area \: of \: parallelogram = l \times h}}$

$\large{ \green{ \: perimeter \: of \: rectangle = 2x(l \times b)}}$

$\large{ \blue{perimeter \: of \: parallelogram = 2x(l + b)}}$

hope its help u