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Consider two congruent square prisms each rectangular face of prism A has a width of 2x+3 and each rectangular face of prism B had a length of 4x+6 if each rectangular face of prism A has and area of 25x+25 what is the volume of prism B (round to the nearest whole number)

Respuesta :

Answer:

Step-by-step explanation:

prism A side area is square of side length

(2x + 3)² = 25x + 25

4x² + 12x + 9 = 25x + 25

4x² - 13x - 16 = 0

x = (13 ±√(13² - 4(4)(-16))) / (2(4))

positive answer is

x = (13 +√425)/8 which is approximately 4.20194...

so side length of B is

4((13 +√425)/8) + 6  which is approximately 22.80776...

Volume is side length cubed

V = (4((13 +√425)/8) + 6)³ which is approximately 11,864.4643...

V = 11,864 units³

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