Question

A triangle has an area of 600 sq cm. Find the length of the base, if the corresponding base is 3 times of it's height.​

Answer 1

To find : length of base .

Given : area of triangle = $600\ cm ^{2}$ , corresponding base is $3$  times of it's height.​

Solution :  

• Let height of triangle be $x$ .
• Then according to given condition ,

        base of triangle  =  $3x$

• We know , that area of triangle is given by ,

        Area of triangle = $\frac{1}{2} \times base \times height$

           $600 = 3x \times x \\600 = 3x^{2} \\x^{2} = \frac{600}{3} \\x^{2} = 200 \\x = 14.14$

• Height = $14.14 \ cm$  
• Base = $3x = 3 \times 14.14 = 42.42\ cm$

Hence , length of base of triangle is $42.42 \ cm$ .