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3 years ago

A triangular flag has an area of 22 cm². Jon measures the height as 8 cm, what is the base length?

1 answer:

4 0

The base length is 5.5 cm.

Explanation:

Area of triangle = base x height x 1/2

Let b cm be the base length of the triangular flag.

22 = b x 8 x 1/2

22 x 2 ÷ 8 = b

b = 44 ÷ 8

b = 5.5

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Answer:

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Step-by-step explanation:

Let's start by using distributive multiplication:

$(a\pm b)(c\pm d)=ac\pm ad \pm bc \pm bd$

So:

$(5x-4)(3x+7)=15x^2+35x-12x-28\\\\$

Grouping like terms:

$15x^2 +(35x-12x)-28\\\\15x^2+23x-28$

Now, $15x^2+23x-28$ is equal to:

$15x^2-ax-b$

In this sense:

$15x^2+23x-28=15x^2-ax-b$

In order to satisfied the equality:

$23x=-ax\hspace{10}(1)\\\\and\\\\-28=-b\hspace{10}(2)$

Hence, from (1), let's solve for a:

$23x=-ax\\\\-a=\frac{23x}{x} \\\\-a=23\\\\a=-23$

And from (2), let's solve for b:

$-28=-b\\\\b=28$

Let's verify the result evaluating the values of a and b into the original equation:

$(5x-4)(3x+7)=15x^2+23x-28=15x^2 -ax -b\\\\(5x-4)(3x+7)=15x^2+23x-28=15x^2 -(-23)x -(28)\\\\(5x-4)(3x+7)=15x^2+23x-28=15x^2 +23x -28$

As you can see, the values satisfy the equation, therefore, we can conclude they are correct.

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3 years ago

30 POINTS!!!!!!!

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