+76 The length of a picture is 4/3 times its width. It is placed in a picture frame of uniform width of 2 cms. If the are of the frame is 100 sq.cms., what are the dimensions of the picture?
+118667 Let the picture be 4z by 3z cm
The frame is 2 cm bigger on all sides so it is 4z+4 and 3z+4 cm
Area of frame
A=(4z+4)(3z+4) = 12z^2 + 16z + 12z + 16 = 12z^2 + 28z + 16
12z^2 + 28z + 16 =100
12z^2 + 28z -84 =0
6z^2 + 14z -42 =0
3z^2 + 7z -21 =0
\(z = {-7 \pm \sqrt{49+252} \over 6}\\ z = {-7 \pm \sqrt{301} \over 6}\\ z>0 \;\;so\\ z = {-7 + \sqrt{301} \over 6}\\ z = {-7 + \sqrt{301} \over 6}\\ z\approx 1.72489\)
3z=5.1746
4z=6.8996
So, if I have understood the question properly then the pic is approx 5.17 by 6.90 cm
