Question

ABCD is a rectangle. If AB + BC = 14 cm and AC + BD = 20 cm, then the length BC of the rectangle is: /

Answer 1

Bc length is 7cm .
half of 14 cm.

Answer 2

THANKS FOR THE QUESTION !

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ANS :

....................... 6CM .......................

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GIVEN :

=> ABCD IS A RECTANGLE .

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LENGTHS :

=> AB

=> CD

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BREADTHS :

=> AD

=> BC

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DIAGONALS :

=> AC

=> BD

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GIVEN INFO :

=> AB + BC = 14 CM

=> LENGTH ( L ) + BREADTH ( B ) = 14 CM

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=> AC + BD = 20 CM

=> DIAGONAL + DIAGONAL = 20 CM

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=> BUT DIAGONALS OF RECTANGLE ARE CONGRUENT :

SO,

=> 2 * DIAGONAL = 20

=> 1 DIAGONAL = 20 / 2

=> DIAGONAL = 10CM

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=> AS WE KNOW RECTANGLE HAS ITS ALL THE FOUR ANGLES MEASURING 90°

SO ,

=> IN THE ONE RIGHT ANGLED TRIANGLE :

=> L ^ 2 + B ^ 2 = DIAGONAL ^ 2

=> L ^ 2 + B ^ 2 = 10 * 10

=> L ^ 2 + B ^ 2 = 100

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=> BY THE PYTHAGOREAN TRIPLET ,

=> WE COME TO KNOW THAT ,

=> L = 8 CM

=> B = 6CM

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=> BC = BREADTH

SO,

=> BC = 6CM

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HOPE IT WILL HELP U.....

THANKS AGAIN....

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