Question 500684
The area of any triangle is 1/2 the base times the height
let the base = {{{ b }}}
Let the height = {{{ h }}}
given:
(1) {{{ (1/2)*b*h = 27 }}}
(2) {{{ h = 3b }}}
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Substitute (2) into (1)
(1) {{{ (1/2)*b*3b = 27 }}}
(1) {{{ (3/2)*b^2 = 27 }}}
(1) {{{ b^2 = (2/3)*27 }}}
(1) {{{ b^2 = 18 }}}
(1) {{{ b = 3*sqrt(2) }}}
and, since
(2) {{{ h = 3b }}}
(2) {{{ h = 3*3*sqrt(2) }}}
(2) {{{ h = 9*sqrt(2) }}}