Jenifers flower bed is in the shape of a right angle triangle. The shortest side is one/forth of the second shortest side. if the area is 18sqaured what are the lengths of ALL THREE SIDES?
I NEED A ANSWER ASAP! PLEASE
short side --- x
longer side ---- 4x
area = (1/2) base x height
(1/2)(x)(4x) = 18
2x^2 = 18
x^2 = 9
x = √9 = 3
short side = 3, longer side = 12
let the hypotenuse be h
h^2 = 3^2 + 12^2 = 153
h = √153 or appr 12.37
To find the lengths of all three sides of Jennifer's flower bed, we can use the given information about the area and the relationship between the sides.
Let's assume the shortest side of the triangle is represented by the variable x. According to the given information, the second shortest side would be 4x, as it is four times the length of the shortest side.
Now, we know that the area of a right-angled triangle is given by the formula: Area = (1/2) * base * height.
In this case, the base and height of the triangle would be x and 4x respectively. So, we can write the equation for the area as:
18 = (1/2) * x * 4x
To solve this equation for x, we first multiply the coefficients and simplify:
18 = 2x^2
Next, we divide both sides of the equation by 2:
9 = x^2
Taking the square root of both sides:
x = ±√9
Thus, we find two possible values for x: x = 3 and x = -3.
Since a length cannot be negative in this context, we consider x = 3 as the valid solution.
Now, we can find the lengths of all three sides:
Shortest side: x = 3 units
Second shortest side: 4x = 4 * 3 = 12 units
Hypotenuse (longest side): By using the Pythagorean theorem, we know that the hypotenuse is given by √(x^2 + (4x)^2). Substituting the value of x, we get:
Hypotenuse: √(3^2 + (4 * 3)^2) = √(9 + 144) = √153 ≈ 12.37 units (rounded to two decimal places)
Therefore, the lengths of all three sides of Jennifer's flower bed are approximately:
Shortest side: 3 units
Second shortest side: 12 units
Hypotenuse: 12.37 units