3 years ago

15 POINTS!!! The perimeter of a rectangle is 20 units. If the width is 3/4 of the length what is the width of the rectangle?

Mathematics

1 answer:

sineoko [7]3 years ago

5 0

Answer:

5 5/7 units

Step-by-step explanation:

Length = x

Width = 3/4 x

Perimeter = 20 units

2( x + 3/4 x) = 20

x + 3/4 x = 10

7/4 x = 10

x = 40/7 = 5 5/7 units

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Answer:

$\large\boxed{x=-\dfrac{7-\sqrt{97}}{4}\ \vee\ x=-\dfrac{7+\sqrt{97}}{4}}$

Step-by-step explanation:

$ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\\text{if}\ \Delta0,\ \text{then an equation has two solutions:}\ x=\dfrac{-b\pm\sqrt\Delta}{2a}\\\\\text{We have:}\\\\-2x^2-7x+10=4\qquad\text{subtract 4 from both sides}\\\\-2x^2-7x+6=0$

$a=-2,\ b=-7,\ c=6\\\\\Delta=(-7)^2-4(-2)(6)=49+48=97>0\\\\\sqrt\Delta=\sqrt{97}\\\\x=\dfrac{-(-7)\pm\sqrt{97}}{2(-2)}=\dfrac{7\pm\sqrt{97}}{-4}=-\dfrac{7\pm\sqrt{97}}{4}$