Question

Find the base of an obtuse angle triangle of area 24.5 ${\text{m}}^2,$ if the height of a triangle is 7 m.

• A. 14 m
• B. 21 m
• C. 7 m
• D. 10 m

Answer 1

The correct option is C 7 m

Let's draw an obtuse angle triangle and name its vertices as $ABC$.
Draw a perpendicular $AD$ from vertex $A$ to the base $BC$ by extending $BC$ to $D$.
Given,
Area of a triangle $=24.5{\text{m}}^2$
Height of a triangle$=AD=7$ m

Let base of a triangle be $=BC$ m

Let consider a triangle $△ABC$ as shown.
As we know,
$\text{Area of}△ABC=\frac{1}{2}\times \text{Base}\times \text{Height}$
$\Rightarrow 24.5=\frac{1}{2}\times BC\times 7$
$BC=\frac{49}{7}=7$ m

Option (c) is correct.