Question

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.

Answer 1

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

$a-b=6$

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

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