The length of the rectangle is 5cm less than thrice its width. Find the dimensions of the rectangle if its area is 112cm²?

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The length of the rectangle is 5cm less than thrice its width. Find the dimensions of the rectangle if its area is 112cm²?

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Answer 1 · 2015-09-06T12:15:51

Length: $"16 cm"$
Width: $"7 cm"$

Explanation:

First, start by writing the formula for the area of a rectangle of width $w$ and length $l$

$color(blue)(A = l * w)$

Now, you know that if you triple the rectangle's width and subtract 5 cm from the result, you get the rectangle's length.

This means that you can write

$l = 3 * w - 5$

Since you know that the area of the rectangle is equal to $"112 cm"""^3$ , you can write a second equation using $l$ and $w$

$(3w - 5) * w = 112$

$3w^2 - 5w = 112$

$3w^2 - 5w - 112 = 0$

Use the quadratic formula to find the two solutions to this quadratic equation

$w_(1,2) = ((-5)) +- sqrt((-5)^2 - 4 * 3 * (-112))/(2 * 3)$

$w_(1,2) = (5 +- sqrt(1369))/6$

$w_(1,2) = (5 +- 37)/6$

Since $w$ represents the width of the rectangle, the negative solution will have no physical significance. This means that the only valid solution to this quadratic is

$w = (5 + 37)/6 = 42/6 = color(green)("7 cm")$

The length of the rectangle will be

$3 * 7 - 5 = 21 - 5 = color(green)("16 cm")$

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The length of the rectangle is 5cm less than thrice its width. Find the dimensions of the rectangle if its area is 112cm²?

1 Answer

Explanation:

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