What is the area of the right angle triangle if the hypotenuse is 9 and one of the sides is 3

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Let ABC be a right angle triangle at B:

Then, AC is the hypotenuse and AB and BC are the legs.

Given that AC = 9

and one of the sides (BC) = 3

We need to find the area.

We know that the area of the triangle is given by:

A = (1/2)* base * height

   = (1/2)* BC * AB

We need to calculate the length of AB

We know that:

AC^2 = AB^2 + BC^2

==> AB^2 = AC^2 - BC^2

                 = 9^2 - 3^2 = 81 -9 = 72

==> AB = sqrt72 = 6sqrt2

Now we will substitute into the area.

==> A = (1/2)*3 * 6sqrt2

            = 9sqrt2 = 12.73 square units.

Then, the area of the triangle is 9sqrt2 = 12.73 square units.

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial