The area of a triangle is 48 cm² . If its height is greater then the base by 4 cm find the base?​

Question

The area of
a triangle is 48 cm² . If its
height is
greater then the base by 4 cm find
the base?​

in progress 0
Kylie 5 days 2021-09-14T01:50:11+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-14T01:51:26+00:00

    \;\;\underline{\textbf{\textsf{ Given:-}}}

    • Area of the triangle = 48 cm

    • It’s height is grater than the base

    by 4.

    \;\;\underline{\textbf{\textsf{ To Find :-}}}

    • Base of the triangle

    \;\;\underline{\textbf{\textsf{ Solution :-}}}

    Let the base be x cm.

    Given that,

    • Its height is greater than its base by 4.

    Then, the height of the triangle will be

    = (x +4) cm

    \underline{\:\textsf{ As  we know that  :}}

    \tt{\small{\boxed{\bold{\bold{\green{\sf{Area\:of\:Triangle=\dfrac{1}{2}\times{b}\times{h}}}}}}}}

    \underline{\:\textsf{ Now, put the given values in the formula :}}

    \longrightarrow  \tt{48=\dfrac{1}{2}\times{x}\times{(x+4)}}

    \longrightarrow \tt{48=\dfrac{1}{2}\times{{x}^{2}}+4x}

    \longrightarrow \tt{48\times{2}={x}^{2}+4x}

    \longrightarrow \tt{96={x}^{2}+4x}

    \longrightarrow \tt{{x}^{2}+4x-96}

    (By splitting Middle Term)

    \longrightarrow \tt{{x}^{2}+4x-96=0}

    \longrightarrow \tt{{x}^{2}+12x-8x-96=0}

    \longrightarrow \tt{x(x+12)-8(x+12)=0}

    \longrightarrow \tt{(x-8)(x+12)=0}

    \;\;\underline{\textbf{\textsf{ Hence-}}}

    \bf{ \longrightarrow x   = 8}

    Or,

    \bf{ \longrightarrow x  = -12}

    Here, remember that base can’t be negative. Therefore, base of the triangle will be 8 cm.

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    0
    2021-09-14T01:52:06+00:00

    Answer:

    Base is 8

    Step-by-step explanation:

    1/2*b*(b+4)=48

    b*(b+4)=96

    b² +4b=96

    From here you can solve quadratic or put value, so put a value which can take nearer to 96 so I took 8 and it will satisfy the equation.

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