The base of a triangle is 4 cm greater than the height. The area is 30 cm^2. How do you find the height and the length of the base?

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Answer 1 · 2017-01-02T06:43:21

Height is $6$ $cm.$ and base is $10$ $cm.$

Area of a triangle whose base is $b$ and height is $h$ is $1/2xxbxxh$ .

Let the height of given triangle be $h$ $cm$ and as base of a triangle is $4$ $cm$ greater than the height, base is $(h+4)$ .

Hence, its area is $1/2xxhxx(h+4)$ and this is $30$ $cm^2$ . So

$1/2xxhxx(h+4)=30$

or $h^2+4h=60$

i.e. $h^2+4h-60=0$

or $h^2+10h-6h-60=0$

or $h(h+10)-6(h+10)=0$

or $(h-6)(h+10)=0$

$:.h=6$ or $h=-10$ - but height of triangle cannot be negative

Hence height is $6$ $cm.$ and base is $6+4=10$ $cm.$