## anonymous 5 years ago Solve for the variable given the surface area S of the right prism or right cylinder.

1. anonymous

Lets start with the Triangular prism. How many sides does it have? I can see there are two isosceles triangles and three rectangles. Do you agree with these basic facts?

3. anonymous

yea

We are to solve for x which is indicated in the diagram. We are given that one leg of the isosceles triangle is 6 cm, the tick marks indicate that both legs are the same (6 cm) We are also given the total surface area is 97.5 cm sq. This if plenty of information and we can figure out what x is. set up equations for all 5 sides and their sum will be 97.5 sq cm.

The area of the 2 triangle shaped pieces is simply computing the area for the triangle A=BH/2 6*6/2=36/2=18 sq cm. Since their are two sides double that for 36 sq cm. The area of the base and left side is 6x. Double that as their are two:.. 12x That takes care of four sides, but we have one left, the inclined one on the right. First compute the the edge that is the hypotenuse of the triangular shaped sides:$6^{2}+6^{2}=h ^{2}$ $72=h ^{2}$ $\sqrt{72}=h$ $h=\sqrt{36\times2}$$6\times \sqrt{2}$

6. anonymous

$6\times \sqrt{2}\approx1.41$

The area of the last side is $6x \times \sqrt{2}$Now add these 5 sides: 36+12x+6xsqrt2=97.5 $6x \sqrt{2}+12x=97.5-36$ $6x \sqrt{2}+12x=61.5$ Factor out the 6x$6x(\sqrt{2}+2)=61.5$ Solve for x $x =(61.5)\div6(2+\sqrt{2})$ You can take it from here.

8. anonymous

x=.33

$6\times \sqrt{2}=8.485$

10. anonymous

i dont understand square roots

x=18 m

Use your calculator or is it permitted?

13. anonymous

i can use my calculator but it doesnt have the sqaure root symbol

O.K You need to get a scientific calculator. sq root of 2 is approximately 1.414

Good luck, I need to take a break.

18 cm

17. anonymous

okay thank you