One leg of a triangle is 28 inches longer than the smaller leg, and the hypotenuse is 32 inches longer than the smaller leg. Find the lengths of the sides of the triangle.

The sides of the triangle are 20 in, 48 in and 52 in

Explanation:

Given:

Let x be the length of smaller leg

Hypotenuse, H = x + 32

Height, h = x + 28

Length of the sides of a triangle = ?

If the triangle is a right angle triangle then we use pythagoras theorm to solve the question.

So,

(Hypotenuse)² = (height)² + (Base)²

(x + 32)² = (x + 28)² + (x)²

x² + 1024 + 64x = x² + 784 + 56x + x²

240 + 8x - x² = 0

x² - 8x - 240 = 0

Solving the quadratic equation:

x² + 12x - 20x - 240 = 0

x(x+12) - 20(x+12) = 0

(x-20) (x+12) = 0

(x-20) = 0

x = 20 in

Hypotenuse, H = x + 32

                    H = 20 + 32 in

                    H = 52 in

Height, h = x + 28

            h = 20 + 28 in

            h = 48 in

Therefore, the sides of the triangle are 20 in, 48 in and 52 in

sides of triangle is 20 inches , ( 20 +28) = 48 inches , ( 20 +32 ) = 52 inches !

Step-by-step explanation:

Here we have , one leg of a triangle is 28 inches longer than the smaller leg, and the hypotenuse is 32 inches longer than the smaller leg. We need to Find the lengths of the sides of the triangle. Let's find out:

Let the smaller side be x  ,So

one leg of a triangle is 28 inches longer than the smaller leg

We have the following length of side as :

⇒

the hypotenuse is 32 inches longer than the smaller leg

We have the following length of hypotenuse as :

⇒

Now , By Pythagoras Theorem :

⇒

⇒

⇒

Simplifying we get :

⇒

⇒

⇒

⇒

⇒

Taking square root both sides we get :

⇒

Since , side can't be negative hence :

⇒

⇒

Therefore , sides of triangle is 20 inches , ( 20 +28) = 48 inches , ( 20 +32 ) = 52 inches !

boxplot e is the answer

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: