A triangle has one side of length 10 cm and another side of length x cm - Junior Cycle Mathematics - Question 11 - 2019

The triangle in Diagram A is a scalene triangle.

Reason: All sides are different lengths (10 cm, 5 cm, and 11 cm).

The axis of symmetry is a vertical line running through the vertex of the parabola, positioned at x = 6. The line can be drawn as a dashed line from the top of the graph down to the x-axis.

To estimate the area of the triangle in Diagram A using point A on the graph, find the corresponding y-value at x = 5. According to the graph, this area is approximately 25 cm².

At x = 9 cm, the area of the triangle in Diagram B can be found on the graph. The estimated area can be noted and point B should be plotted at this coordinate.

To construct the triangle, start by drawing a segment of 10 cm. From either endpoint, use a compass to draw arcs of 8 cm from each endpoint, creating intersections. Connect the intersection points to form the triangle and label the sides accordingly.

Using the theorem of Pythagoras, we have:

$h^2 + 5^2 = 8^2$
$h^2 + 25 = 64$ $h^2 = 39$
$h = ext{sqrt}(39) \approx 6.2 ext{ cm}$ Therefore, the height h is approximately 6.2 cm, correct to one decimal place.