Question

The base of a right-angled triangle is 8m and its hypotenuse is 10 m. Then its area is
\[
  A.\;\;\;\;\;48{m^2} \\
  B.\;\;\;\;\;40{m^2} \\
  C.\;\;\;\;\;30{m^2} \\
  D.\;\;\;\;\;24{m^2} \\
  \]

Answer 1

Hint: We have to use Pythagoras theorem and find the other side of the triangle. Then we can calculate the area of the triangle using the equation for area of a triangle \[Area = \dfrac{1}{2}base \times height\] .

Complete step-by-step answer:
Draw a right-angled triangle and mark the given sides. It is the most important step in solving problems in Geometry.

As we know pythagoras theorem , ${a^2} + {b^2} = {c^2}$
(where c is the hypotenuse and a and b are other sides of the triangle)
Using pythagoras theorem,
We get, ${b^2} = {c^2} - {a^2}$
By substituting the values as in the question, we get ${b^2} = {10^2} - {8^2} = 100 - 64 = 36$
We know that \[{6^2} = {\text{ }}36\]
Taking the square root, we get, $b = 6$.
Now for area , we use the equation \[Area = \dfrac{1}{2}base \times height\]. As the given triangle is right-angled, base and height are the two sides other than the hypotenuse (non- hypotenuse sides).
So,$Area = \dfrac{1}{2} \times a \times b = \dfrac{1}{2} \times 6 \times 8 = 24{m^2}$
Hence, the area of given triangle is \[24{m^2}.\]
Therefore, the correct answer is option D.


Note: While solving problems in geometry, always visualize the problem and draw the figure with labeling on our notebook. Ideas about square and square roots of numbers are also important for solving this problem. Types of errors that can occur are, taking the sides incorrectly and error in calculations. Errors can be reduced by drawing appropriate figures in geometry.