Examkin

Question

Difficulty: MediumTriangles and Pythagorean Theorem

A right triangle has a hypotenuse that measures 2020 centimeters and a base that measures 1212 centimeters. What is the area of this triangle?

  1. A
    48 cm248\text{ cm}^2
  2. B
    120 cm2120\text{ cm}^2
  3. 96 cm296\text{ cm}^2Answer
  4. D
    192 cm2192\text{ cm}^2

Answer

The area of the right triangle is 96 cm296\text{ cm}^2.
To find the area of a right triangle, you need both the base and the height (the two legs). The Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2) reveals the missing height is 1616 cm because 162+122=20216^2 + 12^2 = 20^2. Using the area formula (A=12bhA = \frac{1}{2}bh), we multiply 12×12×16\frac{1}{2} \times 12 \times 16 to get 96 cm296\text{ cm}^2.

Step-by-Step Solution

1
Use the Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2) to find the missing height (the other leg).
a2+122=202a^2 + 12^2 = 20^2
The area formula requires the base and the height. We are given the hypotenuse (2020) and the base (1212).
2
Solve for the missing height (aa).
a2+144=400⇒a2=256⇒a=16a^2 + 144 = 400 \Rightarrow a^2 = 256 \Rightarrow a = 16 centimeters.
Subtracting 144144 from 400400 gives 256256, and the square root of 256256 is 1616.
3
Calculate the area of the triangle using the formula A=12bhA = \frac{1}{2}bh.
A=12×12×16=96 cm2A = \frac{1}{2} \times 12 \times 16 = 96\text{ cm}^2.
Substituting the base (1212) and the newly found height (1616) into the area formula gives the final answer.

Key Concept

Applying the Pythagorean theorem to find a missing side length, then calculating the triangle's area.
Estimated Time:1m 0s
Rate this question

Topics

Triangles and Pythagorean Theorem

More questions from this topic