Question

Draw a triangle ABC right angled triangle at B in which AC=10cm, AB= 8cm

Answer 1

Answer:

Step-by-step explanation:

Since median of a triangle divides it into 2 triangles of equal area

Ar( tri ADB) = Ar ( tri ADC)

Ar(triADB)= √{(15+x)/2} {(15+x)/2 - 7} {(15+x)/2 -8} {(15+x)/2 - x}

=> Ar( tri ADB) = 1/4√{(x²-1)(15²-x²) }. . . . . . . LHS

Ar( triADC) = √{(17+x)/2} {(17+x)/2 -10} {(17+x)/2 - 7} {(17+x)/2 - x}

=> Ar(triADC)= 1/4√{(17²-x²)(x² -9)} . . .. . . . .RHS

LHS = RHS

=> (x²-1)(15²-x²) = (17² - x²)(x² -9)

=> 225x²-225-x^4+x² = 289x²-2601-x^4+9x²

=> 226x²-225 = 298x² -2601

=> 72x² = 2376

=> x² = 33

=> x= √33

=> median AD = √33

Centroid divides each median in the ratio 2:1

AG/GD = 2/1

=> AG = 2√33/3 = 3.83 cm

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Answer 2

Answer:

Step-by-step explanation: