So there's a right angled triangle and it has another small triangle on the top and the right side is 10cm long (including the side of the small triangle). 10-x is bc. I know the base is 3+2xcm.
[bc] is the same as [be]. [cd] is 3 cm more than twice the length of [be]. Find the length of [be].
To find the length of [be], let's break down the given information and solve step by step.
1. We know that [bc] is the same as [be], which means the length of [bc] is equal to the length of [be].
2. We also know that [cd] is 3 cm more than twice the length of [be]. So the length of [cd] can be represented as 2[be] + 3.
3. The length of the hypotenuse of the right-angled triangle is given as 10 cm, and one of the sides of the triangle (the base) is given as 3 + 2x cm.
4. Using the Pythagorean theorem, we can relate the lengths of the sides of the right-angled triangle:
(3 + 2x)^2 + [be]^2 = 10^2
5. Simplifying the equation:
9 + 12x + 4x^2 + [be]^2 = 100
6. Rearranging the equation:
[be]^2 + 4x^2 + 12x - 91 = 0
7. Now, we have two equations:
[bc] = [be]
[cd] = 2[be] + 3
8. We can substitute [be] into the equation for [bc]:
10 - x = [be]
9. Substitute [be] into the equation for [cd]:
[cd] = 2(10 - x) + 3
10. Now, we can substitute [be] and [cd] into the equation from step 6:
(10 - x)^2 + 4x^2 + 12x - 91 = 0
11. Solve the quadratic equation to find the value of x.
12. Once you have found the value of x, substitute it back into the equation for [be] to determine its length.
Following these steps, you should be able to find the length of [be].