Question

The area of a right triangle is 50. One of its angles is 45°. Find the lengths of the sides and hypotenuse of the triangle. pls answer fastly

Answer 1

Answer:

The triangle is right and the size one of its angles is 45°;

the third angle has a size 45° and therefore the triangle is right and isosceles.

Let x be the length of one of the sides and H be the length of the hypotenuse.

Area = (1/2)x2 = 50 ,

solve for x: x = 10

We now use Pythagora to find H:

x2 + x2 = H2

Solve for H: H = 10 √(2)

Step-by-step explanation:

One of the acute angles of given right triangle = 45 deg

=> the right triangle is isosceles triangle

=> 2 legs of the triangle are equal

Let each side be 'h' unit

& area of right triangle = 50 sq unit

1/2 * h * h = 50

=> h^2 = 100

=> h = 10 unit

Hence hypotenuse = √( 10^2 + 10^2) = √200

= 10 √2

So, sides are each 10 units & hypotenuse = 10 √2 unit