Question

the base of a triangle is 4 metre longer than the height. find the height if the area of the triangle is 16 square meters. ​

Answer 1

Given : the base of a triangle is 4 meter longer than the height.

the area of the triangle is 16 square meters.

To find:  the height  

Solution:

Assume that Height of the triangle = x m

base of a triangle is 4 meter longer than the height.

=> Base of the triangle = x + 4  m

Area of  a Triangle = (1/2) * Base * height

= (1/2) *(x + 4) x   sq m

Area of Triangle = 16  sq m

Equate area of triangle

=>  (1/2) *(x + 4) x = 16

=> x² + 4x  = 32

=> x² + 8x - 4x  - 32 = 0

=> x( x + 8) - 4(x + 8) = 0

=> (x + 8)(x - 4) = 0

=> x = - 8  or 4

Length can not be negative  

so x = 4

Hence Height = 4 m  

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Answer 2

$formula \: \: h = 2 \: \frac{a}{b}$

$(2) = \frac{16m {}^{2} }{4m}$

$height \: = 8$

$so \: the \: answer = 8m$

$to \: check \: the \: answer,$

$formula \: \: a = \frac{bh}{2}$

$\frac{4m \: 8m}{2} = \frac{32m}{2}$

$area \: = \: 16m {}^{2}$

$hence, the \: height \: of \: the \: triangle \: is \: 8m$