Answer to Question #157706 in Trigonometry for mohammed Alsaedi

Question

Ali is building a theater in the man-cave in his new house. He cannot recall the exact dimensions, but he knows that the length is 4 feet longer than the width, and the area is 525 square feet. Help Ali and the contractor solve for the length and width of his theater. Show all of your work and explain your answer.

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Answer 1

(i). Let length be L ft.

(ii). Let width be W ft.

(iii). Given length = 4 + Width

Length= 4 + Width

Area = 525ft

(iv). Length x Width = 525ft

(w+4) w = 525

w² + 4w - 525 = 0

w² + 25w -21w -525 = 0

w ( w + 25 ) - 21 ( w + 25 ) = 0

( w + 25 ) ( w - 21 ) = 0

(v). Since w cannot be negative ;

w = 21 ft

L = 4 + w

= 4 + 21 = 25 ft

Length, L = 25 ft

Width, W = 21 ft