Question

angle ABC is a right angled triangle with angle C =90 degree .find BC if
a) AB =70 cm, AC =15 cm
b)AB = 17 cm ,AC=8cm
c)AB = 10 cm , AC=6cm​

Answer 1

AB=9 cm , AC=15 cm .

1)Applying pythagoras theorem in △ABCAC2=AB2+BC2152=92+BC2225=81+BC2225−81=BC2BC2=144BC=12 cm .

2)As D and E are the mid points of AB and AC .

So , by mid point theoremDE=BC2=122=6 cm .AD=AB2=92=4.5 cm .Area of △ADE=12×DE×AD=12×6×4.5=13.5 cm2 .

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Answer 2

Answer:

1. bc=68.38
2. bc=15
3. bc=8

angle c is 90° so,

${ab}^{2} = {bc}^{2} + {ac}^{2}$

1. ${ab}^{2} = {ac}^{2} + {bc}^{2} \\ {70}^{2} = {15}^{2} + {bc}^{2} \\ 4900 = 225 + {bc}^{2} \\ {bc}^{2} = 4900 - 225 \\ {bc}^{2} = 4675 \\ bc = \sqrt{4675 } \\ bc = 68.38$
2. ${ab}^{2} = {bc}^{2} + {ac}^{2} \\ {17}^{2} = {bc}^{2} + {8}^{2} \\ 289 = {bc}^{2} + 64 \\ {bc}^{2} = 289 - 64 \\ {bc}^{2} = 225 \\ bc = \sqrt{225} \\ bc = 15$
3. ${ab}^{2} = {bc}^{2} + {ac}^{2} \\ {10}^{2} = {bc}^{2} + {6}^{2} \\ 100 = {bc}^{2} + 36 \\ {bc}^{2} = 100 - 36 \\ {bc}^{2} = 64 \\ bc = \sqrt{64} bc = 8$