SOLUTION: the perimeter of the rectangle if the width is twice the root of the length and the area is 250

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Question 1076140: the perimeter of the rectangle if the width is twice the root of the length and the area is 250
Found 3 solutions by mananth, ikleyn, josgarithmetic:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
the width is twice the root of the length and the area is 250
length be x
width = 2sqrt%28x%29
Area = 250
x*2sqrt(x)=250
square both sides
4x^3= 250*250
x^3= 125*125
x = sqrt(125*125)
x=25 the length
width = 2*sqrt(x)
= 2*sqrt(25)
=10 the width



Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
highlight%28Find%29 the perimeter of the rectangle if the width is twice the root of the length and the area is 250.
~~~~~~~~~~~~~~~~~~~


        The answer in the post by @mananth is correct,  but on the way he made errors
        that shocked me.  I afraid that they shoked you,  too.
        Therefore,  I came to present the solution in a correct form.
        Read my solution attentively;  watch every my step and find the differences between
        my solution and that by @mananth.


Let the length be x.

Then the width = 2%2Asqrt%28x%29.

Area = 250:  x%2A2sqrt%28x%29 = 250.

Square both sides

    4x^3 = 250*250,

    x^3 = 125*125 = 5%5E3%2A5%5E3 = 25%5E3,

    x = root%283%2C25%5E3%29 = 25  the length.

    width = 2%2Asqrt%28x%29 = 2%2Asqrt%2825%29 = 2*5 = 10.

    the width = 10.


The perimeter = 25 + 10 + 25 + 10 = 70.    ANSWER

Solved.



Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
---------------------------------------------------------------
the width is twice the root of the length and the area is 250.
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L, length
2sqrt(L), width
L%2A2sqrt%28L%29=250
L%2Asqrt%28L%29=125
L%2AL%5E%281%2F2%29=125
L%5E%283%2F2%29=5%5E3
L%5E%283%2F2%29%2AL%5E%283%2F2%29=5%5E6
L%5E3=%285%5E2%29%5E3
highlight_green%28L=25%29------length

Lw=250------the given area
25w=250
highlight_green%28w=10%29------width

Question asked for perimeter.
2%2A10%2B2%2A25
highlight%2870%29