The length of the base of this triangle is given by b-√(l^2-36)

Posted on

Are you looking for a The length of the base of this triangle is given by b-√(l^2-36), if so? then you are on the right website.

Hopefully the following article can be useful.

✅Question :

The length of the base of this triangle is given by b-√(l^2-36). A second larger triangle is constructed with the same height, its base is twice as long. Find an expression for the length of the hypotenuse of the larger triangle (L) in terms of l. Show all steps of working it out.​

✅Answer :

Let’s start by considering the properties of the two triangles and their bases.

  1. First Triangle:
    • Base: b – √(l^2 – 36)
    • Height: h (not specified, but assumed to be constant for both triangles)
  2. Second Triangle:
    • Base: 2b (twice as long as the base of the first triangle)
    • Height: h (same height as the first triangle)

Both triangles have the same height, so their hypotenuses are related by the Pythagorean theorem.

For the first triangle: Hypotenuse of the first triangle (h1) = √[(base)^2 + (height)^2]

For the second triangle: Hypotenuse of the second triangle (h2) = √[(2b)^2 + (height)^2]

Since h1 = h2 (both triangles share the same height), we can set up an equation:

√[(b – √(l^2 – 36))^2 + h^2] = √[(2b)^2 + h^2]

Now, let’s solve for b in terms of h and l:

  1. Square both sides of the equation to eliminate the square roots.
  2. Expand and simplify the expressions.
  3. Solve for b.

Step 1: [(b – √(l^2 – 36))^2 + h^2] = (2b)^2 + h^2

Step 2: b^2 – 2b√(l^2 – 36) + (l^2 – 36) + h^2 = 4b^2 + h^2

Baca Juga:  suggest a reason for their look for the location of urban settlements remember that settlement that start in particular places for different reasons such as fertile soil water availability mineral job opportunities​

Step 3: Collect the terms involving b on one side of the equation: b^2 – 4b^2 = 2b√(l^2 – 36) + l^2 – 36

Simplify the left side: -3b^2 = 2b√(l^2 – 36) + l^2 – 36

Divide both sides by -3b (assuming b ≠ 0): b = [(l^2 – 36) + 2b√(l^2 – 36)] / (3b)

Now, we can express b in terms of l: 1 = [(l^2 – 36) / (3b)] + 2√(l^2 – 36) / (3b)

Solve for 1 – [(l^2 – 36) / (3b)] to get an expression for b: 1 – [(l^2 – 36) / (3b)] = 2√(l^2 – 36) / (3b)

Now, we can find the expression for the length of the hypotenuse of the larger triangle (L) in terms of l: L = √[(2b)^2 + h^2] L = √[(2[(l^2 – 36) + 2b√(l^2 – 36)] / (3b))^2 + h^2]

This expression for L in terms of l is quite complex and involves b, which itself is defined in terms of l. It may not be possible to further simplify this expression without additional information or numerical values for b, h, and l.

✅Read Also : Calculate the standard deviation and co-efficient of variation

That’s what the sharing JAGOAN ILMU can do, about The length of the base of this triangle is given by b-√(l^2-36). That’s all and thank you for visiting jagoanilmu.net, I hope this is useful and see you again in the next category article.