the area of a triangle is 42 sq cm.its altitude is 7 cm. find its base​

2 thoughts on “the area of a triangle is 42 sq cm.its altitude is 7 cm. find its base​”

1. Answer :–

   • The base of the triangle is 12 cm.

   Given :–

   • The area of a triangle is 42 cm².
   • It’s altitude is 7 cm.

   To find :–

   • It’s base.

   Step-by-step explanation :–

   • In this question, the area of a triangle and the length of it’s altitude has been given to us. We have to find it’s base. For this, we are going to use the formula required for finding the area of a triangle, form an equation using it and then solve it to find our answer!

   Calculations :–

   We know that :-

   [tex]\underline{\boxed{\sf Area \: of \: a \: triangle = \dfrac{1}{2} \times Base \times Altitude}}[/tex]

   Here,

   • Area = 42 cm².
   • Altitude = 7 cm.

   • Let’s take the base as b.

   So let’s use this formula now!

   –––––––––––––––––––––––

   [tex] \underline{\underline{\mathfrak{Substituting \: the \: given \: values,}}}[/tex]

   [tex] \boxed{\tt42 = \dfrac{1}{2} \times b \times 7}[/tex]

   Multiplying 7 by b,

   [tex] \boxed{\tt42 = \dfrac{1}{2} \times 7b}[/tex]

   Multiplying [tex] \sf\dfrac{1}{2} [/tex] by 7b,

   [tex] \boxed{\tt42 = \dfrac{7b}{2}}[/tex]

   Transposing 2 from RHS to LHS, changing it’s sign,

   [tex] \boxed{\tt42 \times 2 = 7b}[/tex]

   Multiplying 42 by 2,

   [tex] \boxed{\tt84 = 7b}[/tex]

   Transposing 7 from RHS to LHS, changing it’s sign,

   [tex] \boxed{\tt\dfrac{84}{7} = b}[/tex]

   Dividing 84 by 7,

   [tex] \overline{\boxed{ \tt12 \: cm = b.}}[/tex]

   –––––––––––––––––––––————————————–

   • Hence, the base is 12 cm.

   Reply

2. Given ,
   the area of a triangle = 42 sq. cm
   altitude = 7 cm

   Solution,
   =area of a triangle =1/2 * base * altitude

   = 42 = 1/2 * base * 7
   = base/2 = 42/7
   = base/2 = 6
   = base = 6*2
   = base = 12 cm

   Reply