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Class 10 Class 12

સમરૂપતા અને પાયથાગોરસ પ્રમેય

bold increment bold space bold ABC

માં

bold angle bold B

કાટકોણ છે.

top enclose bold BD

bold perpendicular bold space top enclose bold AC

અને

bold D bold space bold element of bold space top enclose bold AC bold space bold.

જો

bold AD bold space bold equals bold space bold 4 bold DC

તો સાબિત કરો કે

bold BD bold space bold equals bold space bold 2 bold DC bold.

એક ત્રિકોણની બાજુઓનાં માપ 5, 12 અને 13 છે. સાબિત કરો કે ત્રિકોણ કાટકોણ ત્રિકોણ છે. ત્રિકોણના કર્ણ પરના વેધની લંબાઇ શોધો.

bold increment bold space bold PQR

માં

top enclose bold QM

એ કર્ણ

top enclose bold PR

પરનો વેધ છે. જો

bold PM bold space bold equals bold space bold 8 bold comma bold space bold RM bold space bold equals bold space bold 12 bold space

હોય, તો

bold PQ bold comma bold space bold QR

અને

bold QM

શોધો.

$bold increment bold space bold PQR$ માં $top enclose bold QM bold space bold perpendicular bold space top enclose bold PR$

$bold PM bold space bold equals bold space bold 8 bold comma bold space bold RM bold space bold equals bold space bold 12 bold space bold therefore bold space bold PR bold space bold v bold equals bold space bold PM bold space bold plus bold space bold RM bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold equals bold space bold 8 bold space bold plus bold space bold 12 bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold equals bold space bold 20 bold space$

હવે, $bold PQ to the power of bold 2 bold space bold equals bold space bold PM bold space bold times bold space bold PR$

$bold therefore bold space bold PQ to the power of bold 2 bold space bold equals bold space bold 8 bold space bold cross times bold space bold 20 bold therefore bold space bold PQ to the power of bold 2 bold space bold equals bold space bold 2 bold space bold cross times bold space bold 2 bold space bold cross times bold space bold 2 bold space bold cross times bold space bold 2 bold space bold cross times bold space bold 2 bold space bold cross times bold space bold 5 bold space bold therefore bold space bold PQ bold space bold equals bold space bold 4 square root of bold 10 bold therefore bold space bold QR to the power of bold 2 bold space bold equals bold space bold MR bold space bold times bold space bold PR bold therefore bold space bold QR to the power of bold 2 bold space bold equals bold space bold 12 bold space bold cross times bold space bold 20 bold therefore bold space bold QR to the power of bold 2 bold space end exponent bold equals bold space bold 2 bold space bold cross times bold space bold 2 bold space bold cross times bold space bold 3 bold space bold cross times bold space bold 2 bold space bold cross times bold space bold 2 bold space bold cross times bold space bold 5 bold space bold therefore bold space bold QR bold space bold equals bold space bold 4 square root of bold 15 bold therefore bold space bold QM to the power of bold 2 bold space bold equals bold space bold 8 bold space bold cross times bold space bold 12 bold space bold therefore bold space bold QM to the power of bold 2 bold space bold equals bold space bold 2 bold space bold cross times bold space bold 2 bold space bold cross times bold space bold 2 bold space bold cross times bold space bold 2 bold space bold cross times bold space bold 2 bold space bold cross times bold space bold 3 bold space bold therefore bold space bold QM bold space bold equals bold space bold 4 square root of bold 6 bold space$

bold increment bold space bold ABC bold space

માં

bold m bold space bold angle bold space bold B bold space bold equals bold space bold 90 bold degree bold comma bold space top enclose bold BM bold space bold perpendicular bold space top enclose bold AC bold comma bold space bold M bold space bold element of bold space top enclose bold AC bold space bold. bold space

જો $bold AM bold space bold minus bold space bold MC bold space bold space bold equals bold space bold 7 bold comma bold space bold AB to the power of bold 2 bold space bold minus bold space bold AC to the power of bold 2 bold space bold equals bold space bold 175 bold space$ હોય, તો AC શોધો.