The area of a right triangle whose hypotenuse is 15cm and whose height is 12cm is 54sq. cm.What is its perimeter?
you have a 9-12-15 triangle.
To find the perimeter of the right triangle, we first need to find the lengths of the other two sides.
We are given the height (12 cm) and the hypotenuse (15 cm). We can use the Pythagorean theorem to find the length of the base or the other side:
a^2 + b^2 = c^2
where a and b are the legs of the right triangle, and c is the hypotenuse.
In this case, we have:
12^2 + b^2 = 15^2
144 + b^2 = 225
b^2 = 225 - 144
b^2 = 81
b = √81
b = 9 cm
Now we have the lengths of the two sides: the height is 12 cm and the base is 9 cm.
To find the perimeter, we add up the lengths of all three sides:
Perimeter = height + base + hypotenuse
Perimeter = 12 cm + 9 cm + 15 cm
Perimeter = 36 cm
Therefore, the perimeter of the right triangle is 36 cm.