Question

find the area of a right triangle whose base is 52 cm and hypotenuse is 65 cm

Answer 1

By Pythagoras theorem

Hypotenuse²=base²+hieght².

65²=52²+hieght²

4225-2704 =hieght²

1521=hieght²

39 =Hieght


Area of right angled triangle =base*Hieght/2

Area =39*52/2

Area =39*26

Area =1014cm²

Answer 2

The height of the right triangle with a base of 52 cm and a hypotenuse of 65 cm is 39 cm, and its area is 1014 $cm^{2}$.

The area of a right triangle can be found using the formula:

area = (base * height) / 2.

To find the height, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). In this case, the base is "a" and the height is "b".

The Pythagorean theorem can be written as:

$c^{2}$ = $a^{2}$ + $b^{2}$

So, substituting the given values:

$65^{2}$ = $52^{2}$ + $b^{2}$

Expanding and simplifying:

4225 = 2704 + $b^{2}$

Subtracting 2704 from both sides:

1521 = $b^{2}$

Taking the square root of both sides:

b = 39 cm

Finally, the area of the right triangle is:

area = (52 * 39) / 2 =  $\frac{2028}{2}$= 1014 $cm^{2}$

For more such questions on the area of a right triangle: https://brainly.in/question/12755426

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