A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 6 cm more than the shorter leg and the hypotenuse 12 cm more than the shorter leg. How long should the sides of the triangle be?

18cm, 24cm, 30cm

Step-by-step explanation:

Let x be the length of the shorter leg

(x + 12)² = (x + 6)² + x²

x² + 24x + 144 = x² + 12x + 36 + x²

x² - 12x - 108 = 0

x² - 18x + 6x - 108 = 0

x(x - 18) + 6(x - 18) = 0

(x - 18)(x + 6) = 0

x = 18, -6

x = 18

x + 6 = 24

x + 12 = 30

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: