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

To find the length of the third side when x = 9 cm:

Using the same formula:

$ext{Perimeter} = 10 + 9 + ext{Length of third side} = 26$

Solving for the length of the third side: $ext{Length of third side} = 26 - (10 + 9) = 7 ext{ cm}$

The triangle in Diagram A is a scalene triangle, as all sides are of different lengths.

The axis of symmetry can be drawn as a vertical line at x = 6.5 cm, which divides the graph into two mirror-image halves.

To estimate the area of the triangle in Diagram A using the graph:

At point A (x = 5 cm), from the graph, the estimated area is approximately 25 cm².

Plot the point corresponding to x = 9 cm on the graph and label it as point B.

To construct the triangle:

1. Draw a base of 10 cm.
2. From each end of the base, measure 8 cm and draw arcs to intersect above the base.
3. Connect the intersection point to both ends of the base to form the triangle.

To find h, apply the Pythagorean theorem:

In the isosceles triangle, we split it into two right triangles:

1. The base of each right triangle is 5 cm (half the base).
2. The hypotenuse is 8 cm.

Using Pythagoras: $8^2 = h^2 + 5^2$ $64 = h^2 + 25$ $h^2 = 39$ $h = ext{sqrt}(39) ext{ cm} \\ h ext{ is approximately } 6.2 ext{ cm (to one decimal place)}$