Math, asked by sanidhyapokhrai3633, 10 months ago

The altitude of triangle is 6cm more than its base if the area is 108 cm2 then find the base and height with respect to altitude

Answers

Answered by ButterFliee
12

GIVEN:

  • The altitude of triangle is 6cm more than its base
  • The area of triangle is 108 cm²

TO FIND:

  • What is the base and height of the triangle ?

SOLUTION:

Let the base of the triangle be 'x' cm

Altitude of triangle is 6cm more than its base

  • ALTITUDE = (x + 6) cm

We know that the formula for finding the area of the triangle is:-

\large\bf{\star \: AREA = \dfrac{1}{2} \times base \times height\: \star}

According to question:-

On putting the given values in the formula, we get

\rm{\dashrightarrow 108 = \dfrac{1}{2} \times x \times(x +6)}

\rm{\dashrightarrow 108 \times 2 = x(x+6) }

\rm{\dashrightarrow 216 = x^2 + 6x}

\rm{\dashrightarrow 0 =  x^2 + 6x -216  }

\rm{\dashrightarrow 0 = x^2 +(18-12)x -216}

\rm{\dashrightarrow 0 = x^2 + 18x -12x - 216}

\rm{\dashrightarrow 0 = x(x + 18) -12(x + 18) }

\rm{\dashrightarrow 0 = (x+18) (x-12) }

\rm{\dashrightarrow x = -18 \: (Neglected)}

\bf{\dashrightarrow x = 12 }

The value of 'x' is 12

  • BASE = x = 12 cm
  • HEIGHT = (x+6) = 12+6 = 18 cm

______________________

Answered by Anonymous
0

GIVEN:-

b=12cm

area={48cm^2}

TO FIND:-

h=?

solution:-

WE KNOW THE AREA OF TRIANGLE AS

 =  >  \frac{1}{2}  \times b \times h

now, put the given values.....

 \frac{1}{2}  \times 12 \times h =  {48cm}^{2}

 =  >  \frac{1}{ \cancel2}  \times  \cancel{12} \times h = 48

 =  > 6 \times h = 48

 =  > h =  \frac{ \cancel{48}}{ \cancel 6}

 =  > h = 8cm

so, the height is

 \boxed{8cm}

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