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The length of a rectangular frame is 5 cm more than the width. the area inside the frame is 66 square cm. find the width of the frame

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1 Answer

You know that the area of the frame is 66 square centimeters. You also know that the the length of the frame is 5 more than the width. If you make the width x, then the length equals 5+x. Since you now know the sides and the area, you can plug in the sides into the formula for the area of a rectangle which is A=l*w. When you plug everyting in you get 66=x*(5+x). Multiply out the x and you get 66=5x+x^2. Subtract 66 from both sides and you get x^2+5x-66=0. When you factor this you get (x-11)*(x+6)=0. Then x=11 and -6 but you can't have a negative side so it is just 6. Since you know that the length is 5cm more than the width, then you know that the length has to be 11cm and the width has to be 6cm.

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