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.#