JAMB 1989 · UME · Q40

Angles, triangles & polygons
Trigonometric ratios

Triangle $RST$ is right-angled at $S$ , with $RS = x$ , $ST = y$ and hypotenuse $RT = z$ . If $x : y = 5 : 12$ and $z = 52$ cm, find the perimeter of the triangle.

Worked solution (try it first)

Write $x = 5k$ and $y = 12k$ .
By Pythagoras, $z^2 = 25k^2 + 144k^2 = 169k^2$ , so $z = 13k$ .
$13k = 52$ , so $k = 4$ .
The sides are $x = 20$ cm and $y = 48$ cm.
Perimeter $= 20 + 48 + 52 = 120$ cm, option D.

Report a problem with this question