Question

A triangle has a base of x^1/2 m and a height if x^3/4 m. If the area of the triangle is 16m^2, what are the base and height of the triangle?

Answer 1

Base = 4 m

Height = 8 m

Explanation:

For triangle:

`Base\: (b) = x^{(1)/(2)}\: m\\\\Height \:(h) = x^{(3)/(4)}\: m\\\\ A(\triangle)= 16\:m^2\\\\A(\triangle)= {(1)/(2)}(b)(h)\\\\\implies 16=(1)/(2)(x^{(1)/(2)})(x^{(3)/(4)})\\\\\implies 32= (x^{(2)/(4)})(x^{(3)/(4)})\\\\\implies 2^5=x^{(3+2)/(4)}\\\\\implies 2^5=x^{(5)/(4)}\\\\\implies 2=x^{(1)/(4)}\\\\\implies 2^4=x\\\\\implies x=16\:m`

`Base\: (b) = x^{(1)/(2)}={16}^{(1)/(2)}={(4^2)}^{(1)/(2)}=4\: m`

`Height\: (h) = x^{(3)/(4)}={16}^{(3)/(4)}={(2^4)}^{(3)/(4)}=(2)^3=8\: m`