The length of the hypotenuse of an isosceles right-angled triangle is 24. Find the area of the triangle.
Given:
The length of the hypotenuse of an isosceles right-angled triangle is 24.
To do:
We have to find the area of the triangle.
Solution:
Let the other two sides be $x$.
In the right-angled triangle, by Pythagoras theorem,
$x^2 + x^2 = 24^2$
$2x^2= 576$
$x^2 = 288$
$x=\sqrt{288}$
$x = 12\sqrt2$
Therefore,
Area of the triangle $= \frac{1}{2} \times$ base $\times$ height
Area $= \frac{1}{2}\times12\sqrt2\times12\sqrt2$
$=144\ cm^2$
The area of the triangle is $144\ cm^2$.
Related Articles
- The length of the hypotenuse of an isosceles right-angled triangle is \( 20 . \) Find the perimeter and area of the triangle.
- Prove that $(2, -2), (-2, 1)$ and $(5, 2)$ are the vertices of a right angled triangle. Find the area of the triangle and the length of the hypotenuse.
- The hypotenuse of a right-angled triangle is 25 CM if one of the remaining two sides is 24 cm find the length of its third side.
- Find the Number of Possible Pairs of Hypotenuse and Area to Form Right Angled Triangle using C++
- The two sides of a right-angled triangle are 6 cm and 8 cm. Find the length of the hypotenuse.
- Find the hypotenuse of a right angled triangle with given two sides in C++
- Show that in a right angled triangle, the hypotenuse is the longest side.
- Draw an obtuse-angled triangle and a right-angled triangle. Find the points of the concurrence of the angle bisector of each triangle. Where does the concurrence lie?
- Area of Circumcircle of a Right Angled Triangle?
- The perimeter of an isosceles triangle is $42\ cm$ and its base is ($\frac{3}{2}) times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.
- Find the dimensions of Right angled triangle in C++
- Show that the points \( (1,7),(2,4) \) and \( (5,5) \) are the vertices of an isosceles right angled triangle.
- Draw an obtuse-angled triangle and a right-angled triangle. Find the points of the concurrence of the angle bisectors of each triangle. Where do the points of concurrence lie?
- Swift Program to find the hypotenuse of a right-angled triangle with sides l and b
- The angles of a triangle in the ratio 4:3:14, the triangle is a) Isosceles triangleb) Obtuse trianglec) Equilateral triangled)A right angled triangle
Kickstart Your Career
Get certified by completing the course
Get Started