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2 years ago

What is the range of AB?

Mathematics

1 answer:

lana66690 [7]2 years ago

3 0

a, b, c - sides of a triangle

Therefore:

a + b > c

a + c > b

b + c > a

---------------------------------

We have a = AB, b = 140mi, c = 100mi.

(1) a + b > c

AB + 140 > 100 <em>subtract 140 from both sides</em>

AB > -40 → AB > 0

----------

(2) a + c > b

AB + 100 > 140 <em>subtract 100 from both sides</em>

AB > 40

-----------

(3) b + c > a → a < b + c

AB < 140 + 100

AB < 240

<h3>Answer: 40 < AB < 240</h3>

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<u>Solution: </u>

Given that

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As Length is width minus 8,

Length of the rectangle = x – 8

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$\text{ Area of rectangle }= x\times (x-8)$

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On solving above quadratic equation for x, we get

$\begin{array}{l}{\Rightarrow x^{2}-9 x+x-9=0} \\\\ {\Rightarrow x(x-9)+1(x-9)=0} \\\\ {\Rightarrow (x-9)(x+1)=0}\end{array}$

When $x-9 =9, x = 9$

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3 years ago

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3 years ago

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