Find the height of the triangle whose base is two-thirds of its height and area is \$267 cm^2\$.

The base of triangle is \$b = (2/3) times h\$ and area is \$267 cm^2\$.

The aera of triangle is given by

\$Area = (1/2) times base times height\$

Substitute the values in the formula

\$267 = (1/2) times (2/3)times h times h\$

After simplification

\$ 267 = (1/3) times h^2\$

To isolate 'h', we multiply both sides by 3

\$ 267 times 3 = (1/3) times 3 times h^2\$

After simplification

\$801 = h^2\$

After simplification

\$h = sqrt 801\$

After simplification

\$h = 28.314 cm\$

Answer

Therefore, the height of the triangle is \$28.314 cm\$.