Step-by-step explanation:
✰ [tex] \underline {\underline{ \large{ \tt{G \: I \: V \: E \: N : }}}} \: [/tex]
- Area of a triangle ( A ) = 49 inches²
- Let height of the triangle be ' x '. According to question , base of the triangle is twice the height ( i.e 2x ).
✰ [tex] \underline{ \underline{ \large{\tt{S \: O \: L \: U\: T \: I \: O\: N : }}}}[/tex]
[tex] \boxed{ \large{ \tt{Area \: of \: a \: triangle = \frac{1}{2} \: b \: \times \: h}}}[/tex]
Plug the values and then simplify!
⟶ [tex] \large{ \tt{49 = \frac{1}{2} \times 2x \times x}}[/tex]
⟶ [tex] \large{ \tt{49 = {x}^{2} }}[/tex]
⟶ [tex] \large{ \tt{ {x}^{2} = 49}}[/tex]
⟶ [tex] \large{ \tt{x = \sqrt{49}}} [/tex]
⟶ [tex] \large{ \tt{x = \sqrt{ {(7)}^{2} } }}[/tex]
⟶ [tex] \boxed{\large{ \tt{x = 7 \: inches}}}[/tex]
Again , Replacing values , we get :
[tex] \large{ \tt{Base \: ( \: b \: ) = 2x = 2 \times 7 = \boxed{ \large { \tt{14 \: inches}}}}}[/tex]
Therefore ,
- The base of the triangle is [tex] \large{ \underline{ \tt{14 \: inches}}}[/tex].
- The height of triangle is [tex] \underline{ \large{ \tt{7 \: inches}}}[/tex]
And we're done ! ✔
Hope I helped ! ♡
Have a wonderful day / night ! ツ
[tex] \underline{ \underbrace{ \mathfrak{Carry \: On \: Learning}}}[/tex] !! ✎
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