A right triangle and a square share a side. The hypotenuse of the triangle measures 10 cm. One base of the triangle measures 4 cm. Neither the known base nor the hypotenuse is the side that is shared with the square. Find the area of the square.
To find the area of the square, we first need to determine the length of the shared side.
Let's assume the shared side of the right triangle and the square is "x" cm.
Using the Pythagorean theorem, we can find the length of the other base of the right triangle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, we know that the hypotenuse measures 10 cm and one base measures 4 cm. Let's call the other base "y" cm. Applying the Pythagorean theorem:
10^2 = 4^2 + y^2
100 = 16 + y^2
y^2 = 100 - 16
y^2 = 84
Taking the square root of both sides:
y = √84
Therefore, the length of the other base of the right triangle is √84 cm.
Since the shared side is common to both the right triangle and the square, the length of that side is also √84 cm.
Now, we can calculate the area of the square. The area of a square is given by the formula:
Area = side^2
In this case, the length of the shared side is √84 cm. Therefore, the area of the square is:
Area = (√84)^2
Area = 84 cm^2
So, the area of the square is 84 square centimeters.
Given triangle ABC, the right angle being at B.
Given AC = 10
Given AB = 4
Neither AB nor AC share the side of the square.
Therefore, BC = the side of the square being BC = sqrt(10^2 - 4^2) = 9.1651 making the area of the square 84 sq.cm.