Question

Cile,
How many different (non-congruent) triangles can you draw with two
sides 8 and 6 centimetres and area 12 square centimetres? What if the
area is to be 24 square centimetres?
​

Answer 1

Answer:

There will be two non-congruent triangles with two sides 6 cm and 8 cm, whose area will be 12 cm^2. This is because, if base of the triangle is 6 cm then its height must be 4 cm to get the area =12 cm^2.

(Since, area of a triangle =1/2 x base x height). So, while doing the construction we will have to draw a line parallel to the base, at a distance of 4 cm from it, on which the third vertex of the triangle will lie. Then with one of the vertex of the base as centre if we draw an arc with radius 8 cm. It will intersect the line parallel to the base at 2 points. By joining those 2 points with another vertex of the base we get those two possible triangles.

Now, if area of the triangle =24 cm^2 and

Base =6 cm (say)

Then, height of the triangle =8 cm

(Since, area of a triangle =1/2 x base x height)

Therefore, only one such triangle

Hope this helps..Please mark as brainliest

Answer 2

Answer:

Only one triangle.

Step-by-Step Explanation:

Given,

For the triangle of area of 12 cm² the height from the 8 cm side should be 3 cm.

Then,

Area = $\frac{1}{2}$ x 8 x 3 cm².

Draw a line 8 cm long. Draw another line parallel to it at a distance of 3 cm. Draw a circle of radius 6 cm with one end of the first line as the center. The points where this circle cuts the second line are the third vertex of the triangle.

We can draw two triangles having area 12 cm².

Now,

For the traingle of area 24 cm², the height from the 8 cm side should be 6 cm.

There can only be one triangle of this type.

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