1. ## related rates

A water trough is 4 m long and its cross-section is an isosceles triangle which is 80 cm wide at the top, and the height is 40 cm. The trough is not full. Give an expression for V, the volume of water in the trough in cm3, when the depth of the water is d cm.

V = ??? cm^3

2. Originally Posted by samtheman17
A water trough is 4 m long and its cross-section is an isosceles triangle which is 80 cm wide at the top, and the height is 40 cm. The trough is not full. Give an expression for V, the volume of water in the trough in cm3, when the depth of the water is d cm.
Draw the cross-sectional view, being an upside-down isosceles triangle. Draw the "height" line. Label half of the top with the value for half of the width (being the "base" of the right triangle formed by the "height" line). Label the "height" with the given value.

Draw an horizontal line somewhere in the middle-ish of the triangle, showing the height of the water. Label the height as "h" and (half of) the width as "w". Note the nested, and thus similar, triangles. Use this to solve for h or w in terms of the other variable.

Use the formula for the area of a triangle to create an expression, in terms of the other variable, for the cross-sectional area. Then multiply by the length to get the volume of water.

If you get stuck, please reply with a clear listing of your steps and reasoning so far. Thank you!

3. okay.....thanks...
so i got that the ratio of h/w for the similar triangle is the same ratio as 40/40 for the bigger triangle which equals 1. Am i not supposed to choose any number for my smaller triangle h/w to equal the ratio of 1? for example 20 and 20? how do i figure this out and then how to i put it into an expression?