Question

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? (5 points)

Answer 1

To determine the area of the third square, we need to find the length of its side.

Let the three sides of the triangle be a, b, and c, and let the lengths of the sides of the squares A, B, and C be x, y, and z respectively.

According to the given information, we have the following equations:

Area of square A = x^2 = 18
Area of square B = y^2 = 90

Since the areas of squares A and B are given, we can solve these equations to find the lengths of their sides:

x^2 = 18
x = √18
x ≈ 4.24

y^2 = 90
y = √90
y ≈ 9.49

Now let's consider square C. To have a right angle in the triangle, the sum of the areas of squares A and B should be equal to or greater than the area of square C.

x^2 + y^2 ≥ z^2

Substituting the values of x and y, we get:

4.24^2 + 9.49^2 ≥ z^2
18 + 90 ≥ z^2
108 ≥ z^2

To determine the minimum area of square C, we need to take the square root of both sides:

√(108) ≥ z
z ≥ √108
z ≥ 10.39

Therefore, the minimum area of the third square, area C, would be approximately 10.39 units^2 for the triangle to have a right angle.