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Mathematics

Grade10

Easy

Question

Find the length and the width of a rectangle whose length is 5 cm longer than its width and whose area is 50 cm².

L = 10 cm., W = 5 cm
L = 5 cm., W = 10 cm
L = 25 cm., W = 2 cm
L = 2 cm., W = 25 cm

The correct answer is: L = 10 cm., W = 5 cm

First, the area of this rectangle is given by $L cross times W comma$ meaning that, for this rectangle,
$L cross times W equals 50 comma text or end text left parenthesis W plus 5 right parenthesis W equals 50$

Multiplying this out gives us:
$W squared plus 5 W equals 50$
Which rearranges to:
$W squared plus 5 W minus 50 equals 0$
Second, we factor this quadratic to get our solution:
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell W squared plus 5 W minus 50 equals 0 end cell row cell left parenthesis W minus 5 right parenthesis left parenthesis W plus 10 right parenthesis equals 0 end cell row cell W equals 5 comma negative 10 end cell end table$
We reject the solution $W equals negative 10$
This means that $L equals W plus 5 equals 5 plus 5 equals 10$

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