42. An artist lays down a white triangular background on a building on which she will paint a Penrosetriangle. The triangular area measures 20 ft on each side and will be covered with three layers of primerpaint.a. To the nearest square foot, what is the area of the triangular region to be primed?b. If primer paint covers 200 ft²/gal, how many gallons of primer must be purchased?

Answered: An artist lays down a white triangular…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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42. An artist lays down a white triangular background on a building on which she will paint a Penrose
triangle. The triangular area measures 20 ft on each side and will be covered with three layers of primer
paint.
a. To the nearest square foot, what is the area of the triangular region to be primed?
b. If primer paint covers 200 ft²/gal, how many gallons of primer must be purchased?

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$G i v e n, E a c h s i d e o f a t r i a n g l e = 20 f t G i v e n t r i a n g l e i s e q u i l a t e r a l . (a) A r e a o f a n e q u i l a t e r a l t r i a n g l e = \frac{\sqrt{3}}{4} {(s i d e)}^{2} = \frac{\sqrt{3}}{4} \times 20 \times 20 = \sqrt{3} \times 5 \times 20 = 100 \sqrt{3} = 173 f t^{2} T h u s, a r e a o f t h e t r i a n g u l a r r e g i o n t o b e p r i m e d i s 173 f t^{2}$

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