The area of a triangle , whose base and the corresponding altitude are 15 cm and 7 cm, is equal to area of a right triangle whose one of the sides containing the right angle is 10.5 cm, Find the other side of this triangle.

Ans.= area=15×7=105
105-10.5=00

Area of first triangle = (1/2)(15)(7) = 105/2

area of 2nd triangle = (1/2)(10.5)h

(1/2)(10.5)h = 105/2
10.5h = 105
h = 105/10.5 = 10

thank you

To find the other side of the right triangle, we first need to find the length of the hypotenuse of the right triangle.

We know that the area of the right triangle is equal to the area of the given triangle:
Area of right triangle = 105 cm²

To find the length of the hypotenuse, we can use the formula for the area of a right triangle:
Area of right triangle = (1/2) * base * height

Let's substitute the given values:
105 = (1/2) * 10.5 * height

Now, solve for height:
height = (2 * 105) / 10.5
height = 20 cm

Since the length of one side containing the right angle is 10.5 cm, and the length of the hypotenuse is 20 cm, we can use the Pythagorean theorem to find the length of the other side:
c² = a² + b²

Substituting the given values:
20² = 10.5² + b²

Now solve for b:
b² = 20² - 10.5²
b² = 400 - 110.25
b² = 289.75

Taking the square root of both sides:
b = √289.75
b ≈ 17 cm

Therefore, the length of the other side of the right triangle is approximately 17 cm.