Question 838167
Let {{{ a }}} = the short side of the rectangle
Let {{{ b }}} = the long side of the rectangle
Set up the ratio:
(1) {{{ 5/7 = a/b }}}
You are given that:
(2) {{{ a*b = 140 }}}
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Multiply both sides of (1) by {{{ 7b }}}
(1)) {{{ 5b = 7a }}}
and
Divide both sides of (2) by {{{ a }}}
(2) {{{ b = 140/a }}}
Substitute (2) into (1)
(1) {{{ 5*(140/a) = 7a }}}
(1) {{{ 5*140 = 7a^2 }}}
(1) {{{ a^2 = 5*20 }}}
(1) {{{ a^2 = 100 }}}
(1) {{{ a = 10 }}}
and, since
(2) {{{ b = 140/a }}}
(2) {{{ b = 140/10 }}}
(2) {{{ b = 14 }}}
The sides are 10 cm and 14 cm