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3 years ago

7

The perimeter of a picture frame is 24 inches. If the width of the picture frame is 5 inches, what is the length of the picture

frame?

2 answers:

Fofino [41]3 years ago

8 0

The answer is (8x+36) inches

Zarrin [17]3 years ago

3 0

L=7
2l+2w=24
2l+2x5=24
2l+10=24
2l=14
l=7

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When the sum of \, 528 \, and three times a positive number is subtracted from the square of the number, the result is \, 120. F

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Let $x$ be the unknown number. So, three times that number means $3x$ , and the square of the number is $x^2$

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Then, we have to subtract this number from $x^2$ , so we have

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$x^2 - 3x - 528 = 120 \iff x^2 - 3x - 648 = 0$

This is a quadratic equation, i.e. an equation like $ax^2+bx+c=0$ . These equation can be solved - assuming they have a solution - with the following formula

$x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

If you plug the values from your equation, you have

$x_{1,2} = \dfrac{3\pm\sqrt{9-4\cdot(-648)}}{2} = \dfrac{3\pm\sqrt{9+2592}}{2} = \dfrac{3\pm\sqrt{2601}}{2} = \dfrac{3\pm51}{2}$

So, the two solutions would be

$x = \dfrac{3+51}{2} = \dfrac{54}{2} = 27$

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But we know that x is positive, so we only accept the solution $x = 27$

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