Question

$\Delta$ABC and $\Delta$PQR are similar triangles. If AB = 12 cm, BC = 14 cm, AC = 4 cm, PQ = 6 cm, QR = (x + 2) cm, PR = (y + 3) cm, find the values x and y.
[3 Marks]

Answer 1

Given:
$\Delta$ABC $\sim$ $\Delta$PQR
AB = 12 cm, BC = 14 cm, AC = 4 cm, PQ = 6 cm, QR = (x + 2) cm, PR = (y + 3) cm

We know that corresponding sides of similar triangles are proportional.

$\therefore$ $\frac{AB}{PQ}=\frac{BC}{QR}=\frac{CA}{PR}$ [1 Mark]

$\frac{12}{6}=\frac{14}{x+2}=\frac{4}{y+3}$

$\frac{12}{6}=\frac{14}{x+2}$

$2=\frac{14}{x+2}$

2x + 4 = 14
x = 5 [1 Mark]

$\frac{12}{6}=\frac{4}{y+3}$
$2=\frac{4}{y+3}$
2y + 6 = 4
2y = -2
y = -1 [1 Mark]