Question

the base of a triangle is 7 less than twice its height. If the area of the triangle is 102m^2, find the length of the base.

Answer 1

Answer:

The length of the base will be: 17 m

Step-by-step explanation:

Given the area of the triangle

$A=102\:m^2$

Using the formula of Area of a triangle:

$A=\frac{1}{2}\left(b\times h\right)$

Here,

• 'b' is the base

• 'h' is the height

As the base of a triangle is 7 less than twice its height.

so

$b=2h-7$

so the formula of Area of a triangle becomes

$102=\frac{1}{2}\left(\left(2h-7\right)\times \:h\right)$

$204=h\left(2h-7\right)$

$2h^2-7h=204$

$2h^2-7h-204=0$

$\left(2h+17\right)\left(h-12\right)=0$

$2h+17=0\quad \mathrm{or}\quad \:h-12=0$

$h=-\frac{17}{2},\:h=12$

As height can not be negative, so:

$h=12$ m

Hence, the length of the base:

$b=2h-7$

   $= 2(12)-7$

    $=24-7$

     $= 17$ m

Therefore, the length of the base will be: 17 m