All TV set have screens with the same ratio of height to wid

All TV set have screens with the same ratio of height to width. Paul just bought a new TV that has 27inches screen measured diagonally. If Paul’s old set measured 13.5 inches diagonally, how many times larger (area) is his new screen?

Solution

TV set have screens with the same ratio of height to width therefore l/b =k l =bk

length of diagonal = sqrt(l^2+ b^2) where l is the height and b is the width of new TV

d ^2 = l^2+ b^2 to calculate area using pythagorous theorem triangle l =b

27^2 =b^2(k^2 + 1) --------------1

for old set 13.5^2 = b1^2(k^2 + 1) -----------------2

dividing 1 by 2 we get b/b1 =2

there fore area increased by two times.