Question

A right triangle's height is 3 times the length of its base. if the area of the triangle is 726 cm^2, what is the height

Answer 1

Answer:

22 cm is the height of the right triangle .

Step-by-step explanation:

Area of the triangle = A = $726 cm^2$

Let the base 'b' of the triangle be x

A right triangle's height 'h' is 3 times the length of its base we can also be written as:

= h = 3x

Area of the triangle = $\frac{1}{2}b\times h$

$A=\frac{1}{2}b\times h$

$726 cm^2=\frac{1}{2}\times x\times 3x$

$x^2=\frac{726 cm^2\times 2}{3}$

$x=22 cm$

Height of the right triangle = h = 3x = 3 × 22 cm = 66 cm

Answer 2

Let the length of the base be x.

Height = 3x

Area = 726

$\frac{1}{2} bh$ = 726

$\frac{1}{2}* 3x*x$ = 726

$3 x^{2}$ = 1452

$x^{2}$ = 484

x = 22.

Hence, 

The length of the base is 22 cm.

The height of the triangle is 66 cm.