Question

A triangle has a base of x^1/2

m and a height of x^1/3 m. If the area of the triangle is 16 m². what are the base and height of the triangle?

Answer 1

Base = 8 m

Height = 4 m

Explanation:

Area of triangle

`= (1)/(2) * base * height \\ \\ 16 * 2= {x}^{ (1)/(2) } * {x}^{ (1)/(3) } \\ \\ 32 = {x}^{ (5)/(6) } \\ \\ {2}^(5) = {x}^{ (5)/(6) } \\ \\ ({2}^(2))^{ (6)/(5) } = x \\ \\ x = {2}^{5 * (6)/(5) } \\ \\ x = {2}^(6) \\ \\ base = {x}^{ (1)/(2) } = {({2}^(6))}^{ (1)/(2) } \\ \\ base = {2}^(3) \\ \\ base = 8 \: m \\ \\ \\ height = {x}^{ (1)/(3) } = {({2}^(6))}^{ (1)/(3) } \\ \\ height= {2}^(2) \\ \\ height = 4 \: m`