Question

A prism has volume 100cm^3 and length 8cm. If the cross-section is an equilateral triangle, find the length of a side of the triangle.

Answer 1

Given : 

A prism has volume 100cm^3 and length 8cm. If the cross-section is an equilateral triangle.

To find :

 The length of a side of the triangle ?

Solution :

The volume of the prism = 100 cm³

The length is 8 cm.

Area of the base of prism (cross section) is given by,

$\bf \{Area= \frac{volume}{length} \}$

$\bf \:Area = \frac{100}{8}$

So, area of the equilateral triangle is 12.5cm².

Now,

$\bf \:a² = \frac{ 12.5 \times 4}{ \sqrt{3} }$

$\bf \: a = 28.86$

$\bf \: a = 5.37 \: cm$

Answer 2

Answer: Given: A prism has volume 100cm^3 and length 8cm. If the cross-section is an equilateral triangle, find the length of a side of the triangle.

The volume of the prism = 100 cm^3

The length of the prism is 8 cm.

Area of equilateral triangle or base = volume/length

= 100/8 = 12.5 cm^2

Length of a side of equilateral triangle:

Area of equilateral triangle = (square root of 3/4) * a^2

(12.5cm^2 *4)/Square root of 3 = a^2

28.9 = a^2

Square root of 28.9 = 5.37 cm = a (length of side)