Geometry Practice Test 4

Perimeter of a right angled triangle = 234 m
Sum of other two sides = 234 - 97 = 137 m.
By Pythagoras theorem,
${\left(\mathit{a}\right)}^2+{\left(137-\mathit{a}\right)}^2$ + 137 − a = 97
${\mathit{a}}^2$ +18,769 + ${\mathit{a}}^2$ − 274a = 9,409
2a2 − 27a + 9,360 = 0

${\mathit{a}}^2$ −137a + 4,680 = 0
${\mathit{a}}^2$ − 72a − 65a + 4,680 = 0
(a − 72) (a − 65) = 0
a = 72,65
a = 72, b = 137 − 72 = 65