Question

the frame is 5 inches wider than its height its area is 66 inches squared find the width and the height of the rectangular picture frame

Answer 1

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$given : \\ \\ area = 66 \\ \\ b = l + 5 \\ \\ to \: \: \: find : \: \: \: \: \: length(h) \\ \\ soution: \\ \\ area = lb \\ \\ 66 = l(l + 5) \\ \\ 66 = {l}^{2} + 5l \\ \\ {l}^{2} + 5l - 66 = 0 \\ \\ {l}^{2} + 11l - 6l - 66 = 0 \\ \\ l(l + 11) - 6(l + 11) = 0 \\ \\ (l + 11)(l - 6) = 0 \\ \\ l = - 11 \\ or \\ l = 6 \\ \\ l = - 11 \: \: rejected \\ since \: \: \: lenth \: \: \: cant \: \: be \: \: - ve \\ \\ therefore \\ \\ l = 6 \\ \\ b = l + 5 \\ \\ b = 6 + 5 \\ \\ b = 11 \\ \\ height = 6 \: \: inch$

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