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vovikov84 [41]
3 years ago
15

the volume of a sandbox shaped like a rectangular prism is 48 ft3. the height of the sandbox is 2 feet, the width is w feet and

the length is w + 2 feet. use the formula v= lwh to find the value of w
Mathematics
1 answer:
Effectus [21]3 years ago
3 0
Lwh=v
2*w*(w+2)=48
2w^2+4w=48
w^2+2w-24=0
(w+6)(w-4)=0
w= - 6 or w= 4
Since w cannot be negative, then w=4.
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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= root 2 cm.
Nata [24]

Given CD is an altitude such that AD=BC , AB=3 cm and CD= √2 cm.

Let AD=x, Since given AB=3

                                     AD+DB=3

                                       x+DB = 3

                                        DB = 3-x

Since ΔBCD is rght angle triangle, let's apply Pythagoras theorem

BC^{2} = DB^{2} +CD^{2}

BC^{2} = (3-x)^{2} +(\sqrt{2} )^{2}

BC^{2} =(3-x)^{2} +2

Since given AD=BC,let us plugin BC=x in above step.

x^{2} =(3-x)^{2} +2

x^{2} =9-6x+x^{2} +2

6x=11

x=\frac{11}{6}

Now we know AD=x=\frac{11}{6} and given CD=√2.

Let us apply Pythagoras theorem for ΔACD

AC^{2} =AD^{2} +DC^{2}

AC^{2} = (\frac{11}{6} )^{2} +(\sqrt{2} )^{2}

AC^{2} =\frac{193}{36}

AC=\sqrt{\frac{193}{36} } = 2.315cm

3 0
3 years ago
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