What is the greatest possible area of a triangle with one side of length 7 and another side length 10?

Solution:

A triangle with two given sides has maximum area if these two sides are placed at right angles to each other.

Let, one side of length =10 be the base and the other side of length = 7 be the altitude or height of the triangle.

The area of a triangle is the region enclosed between the sides of the triangle.

Depending on the length of the sides and the internal angles, the area of a triangle varies from one triangle to another.

Area of the triangle = 1/2 × base × height

Maximum possible area of the triangle

= 1/2 × 10 × 7

= 35 units

What is the greatest possible area of a triangle with one side of length 7 and another side length 10?

Summary:

The greatest possible area of a triangle with one side of length 7 and another side length 10 is 35 units.