solve
x^2=121
smaller solution is?
larger solution is?
To solve for x, we need to find the square root of both sides of the equation:
√(x^2) = √121
Simplifying the equation:
x = ±√121
The smaller solution is the negative square root of 121:
x = -11
The larger solution is the positive square root of 121:
x = 11
To solve the equation x^2 = 121, we can take the square root of both sides of the equation.
Taking the square root of both sides, we get:
√(x^2) = √121
The square root of x^2 is x since the square root is the inverse operation of squaring. The square root of 121 is 11, as the square root of a perfect square gives the original number.
So, we have:
x = 11 or x = -11
Therefore, the solutions to the equation x^2 = 121 are x = 11 and x = -11.
The smaller solution is -11, and the larger solution is 11.
To solve the equation x^2 = 121, you can take the square root of both sides:
√(x^2) = √(121)
This simplifies to:
x = ±√121
The square root of 121 is 11, so the solutions are:
x = 11 or x = -11
Therefore, the smaller solution is -11, and the larger solution is 11.
a triangle is drawn and squares are created from the lengths of each side.
square a has an area of 14 units^2 and square b has an area of 60 units^2.
what must be the area of the third square for triangle to have a right triangle
To determine the area of the third square that would make the triangle a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).
Let's designate the sides of the triangle as a, b, and c, with c being the hypotenuse.
We know that square a has an area of 14 units^2, so its side length is √14.
We also know that square b has an area of 60 units^2, so its side length is √60.
By the Pythagorean theorem, we have the following equation:
(√14)^2 + (√60)^2 = c^2
Simplifying:
14 + 60 = c^2
74 = c^2
Taking the square root of both sides:
√74 = c
So, the length of the hypotenuse is √74.
To find the area of the third square, we need to square the length of the hypotenuse:
Area of the third square = (√74)^2
Area of the third square = 74 units^2
Thus, the area of the third square must be 74 units^2 for the triangle to be a right triangle.
if a right triangle has a leg that is 6 ft. long and the hypotenuse is 12 ft. long, how long is the other leg? round to the nearest tenth.
___ft.
To find the length of the other leg of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).
Let's designate the lengths of the legs of the triangle as a and b, and the length of the hypotenuse as c.
We know that one leg is 6 ft long (let's call it a), and the hypotenuse is 12 ft long (let's call it c).
Using the Pythagorean theorem, we have the following equation:
a^2 + b^2 = c^2
Plugging in the known values:
(6 ft)^2 + b^2 = (12 ft)^2
36 ft^2 + b^2 = 144 ft^2
Subtracting 36 ft^2 from both sides:
b^2 = 144 ft^2 - 36 ft^2
b^2 = 108 ft^2
Taking the square root of both sides:
b = √108 ft
Using a calculator, we find that √108 ≈ 10.39.
Thus, the length of the other leg is approximately 10.4 ft.
if a right triangle has legs measuring 10cm and 24cm, how long is the hypotenuse?
____cm
To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that 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 two other sides (legs).
Let's designate the lengths of the legs of the triangle as a and b, and the length of the hypotenuse as c.
We know that one leg measures 10 cm (let's call it a) and the other leg measures 24 cm (let's call it b).
Using the Pythagorean theorem, we have the following equation:
a^2 + b^2 = c^2
Plugging in the known values:
(10 cm)^2 + (24 cm)^2 = c^2
100 cm^2 + 576 cm^2 = c^2
676 cm^2 = c^2
Taking the square root of both sides:
c = √676 cm
Using a calculator, we find that √676 = 26 cm.
Therefore, the length of the hypotenuse is 26 cm.