A garden has the shape of a right triangle with one leg

8
meters longer than the other. The hypotenuse is
8
meters less than twice the length of the shorter leg. What is the length of the shorter​ leg?

Billy charges $15 to mow a yard. He needs at least $200 for the new bicycle that he wants. Write and solve an inequality to find out how many yards must he mow to make at least $200?

A) 11 yards
B) 12 yards
C) 13 yards
D) 14 yards

D) 14

14

To find the length of the shorter leg of the right triangle garden, let's denote the length of the shorter leg as 'x' meters.

According to the problem, the longer leg is 8 meters longer than the shorter leg. Therefore, the length of the longer leg can be expressed as 'x + 8' meters.

The hypotenuse is 8 meters less than twice the length of the shorter leg. So, the length of the hypotenuse can be expressed as '2x - 8' meters.

Now, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs.

Using this theorem, we can write the equation as follows:

x^2 + (x + 8)^2 = (2x - 8)^2

Expanding the equation:

x^2 + (x^2 + 16x + 64) = (4x^2 - 32x + 64)

Combining like terms:

2x^2 + 16x + 64 = 4x^2 - 32x + 64

Subtracting (2x^2 + 32x + 64) from both sides:

0 = 2x^2 - 48x

Dividing both sides by 2x:

0 = x - 24

x = 24

Therefore, the length of the shorter leg of the right triangle garden is 24 meters.

short leg = x

long leg = x+8
hypotenuse = 2x-8
so
{ 2(x-4) }^2 = x^2 + (x+8)^2

4 (x^2 - 8 x + 16)= x^2+x^2+16x+64

4x^2 -32 x + 64 = 2 x^2 +16 x + 64

2 x^2 -48 x = 0
x = 0 works
but
x = 24
*******************
check
24 , 32 , 40
or /8
3 , 4, 5 LOL yes, right triangle

b) 12