Question

find the altitude of a triangle whose area is 42 cm sq and base is 12 cm​

Answer 1

$\textbf{\underline{\underline{Answer :-}}}$

The height of the triangle is 7 cm.

$\textbf{\underline{\underline{Explanation :- }}}$

$\textsf{\underline{\underline{Given :}}}$

Area of the given triangle = 42 sq.cm

Base = 12 cm

$\textsf{\underline{\underline{To find :}}}$

The height of the triangle

$\textsf{\underline{\underline{Solution :}}}$

Consider the altitude/height of the triangle as x

Area of the triangle :

$\tt{\implies \dfrac{1}{2} \times base \times height}$

$\tt{\implies42 = \dfrac{1}{2} \times 12 \times x}$

$\tt{\implies42 = 1 \times 6 \times x}$

$\tt{\implies42 = 6x}$

$\tt{\implies6x = 42}$

$\tt{\implies \: x = \dfrac{42}{6} }$

$\tt{\implies \: x = 7}$

$\boxed{\tt{Height \: = 7cm}}$

$\textbf{\underline{\underline{Verification :-}}}$

$\tt{\implies42 = \dfrac{1}{2} \times 12 \times 7}$

$\tt{\implies42 = 1 \times 6 \times 7}$

$\tt{\implies42 = 42}$

$\boxed{\tt{LHS = RHS}}$

$\therefore$The height of the triangle is 7 cm.

Answer 2

$\mathfrak{Step-by-step\:explanation:}$

Triangle:

• A polygon having three sides.

Altitude:

• The altitude to a side of a triangle is the perpendicular drawn from a vertex to its opposite side.

Let the altitude of a triangle be h cm.

Given :

• Area of the triangle = 42 cm².
• Base = 12 cm.

$\boxed{\bold{Area\:of\:the\;triangle=\dfrac{1}{2}\times Base\times Height}}\\\\\\\implies\bold{\dfrac{1}{2}\times 12\times h=42}\\\\\\\implies\bold{6h=42}\\\\\\\implies\bold{h=\dfrac{42}{6}=7.}\\\\\\\boxed{\boxed{\bold{Altitude=7\:cm.}}}$