Answer to Question #155021 in Geometry for Kinza Tahir

Question #155021

A rectangular picture is 6cm longer than it is wide. A frame 1cm wide is placed around the picture. The area covered by the pictures and frame together is 48cm ² greater than the area of the picture alone. Find the dimensions of the picture. Include a labelled diagram as part of your answer.


1
Expert's answer
2021-01-12T15:00:33-0500

We will note picture's length aa and it's width bb (all in cm). Then we have two equations :

ab=6a-b=6

(a+1)(b+1)ab=48(a+1)\cdot(b+1)-a\cdot b= 48 which gives a+b+1=48a+b+1=48

By solving this system (for example, we can first add these equations to find a, then find b from the first equation) we find a=26.5cm,b=20.5cma=26.5cm, b=20.5cm


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