# The area of a triangle is 15 m^2. The height is 6 m, and the length of the base is #sqrt(3x-5)m. What is the value of x?

##### 1 Answer
May 17, 2018

the answer is $x = 10$

#### Explanation:

the area of triangle equal

$A = 15 {m}^{2}$

the rule of triangle area is

$A = \frac{1}{2} \cdot \left[b a s e \cdot h i g h\right]$

since the high equal $h i g h = 6 m$

the base equal $b a s e = \sqrt{3 x - 5} m$

$A = \frac{1}{2} \cdot \left[b a s e \cdot h i g h\right]$

$15 = \frac{1}{2} \cdot \left[\sqrt{3 x - 5} \cdot 6\right]$

$15 = 3 \cdot \sqrt{3 x - 5}$

$\frac{15}{3} = \sqrt{3 x - 5}$

square both side

$\frac{225}{9} = 3 x - 5$

$3 x = \frac{225}{9} + 5$

$3 x = \frac{225 + 45}{9}$

$3 x = \frac{270}{9}$

$3 x = 30$

$x = 10$