Triangle ABC is a right triangle, where AB and BC are the two legs and AC is the hypotenuse.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
Let's say the length of side AB is x. Then, the length of side BC is also x, since they are both legs of the triangle.
Square A has an area of 18 units^2. Since the length of one side is x, we can write the equation:
x^2 = 18
Square B has an area of 90 units^2. Since the length of one side is x, we can write the equation:
x^2 = 90
Now, we have a system of two equations:
x^2 = 18 ...(1)
x^2 = 90 ...(2)
From equation (1), we can solve for x:
x^2 = 18
x = sqrt(18)
x ≈ 4.2426
From equation (2), we can solve for x:
x^2 = 90
x = sqrt(90)
x ≈ 9.4868
Now, to find the area of square C, which is the square of the hypotenuse AC, we can use the Pythagorean theorem:
AC^2 = AB^2 + BC^2
Substituting the values we found:
AC^2 = (4.2426)^2 + (9.4868)^2
AC^2 ≈ 18 + 90
AC^2 ≈ 108
Therefore, the area of Square C is 108 units^2.
A triangle is drawn and squares are created from the lengths of each side. Square A has an area of 18 units2
and Square B has an area of 90 units2
. What must be the area of the 3rd square for triangle to have a right angle? A standard proof image of the Pythagorean theorem. (5 points)
The area of Square C=
units2
1 answer