Question

Given: AKLM is a trapezoid, AK=13 LM=14, KL=5, AM=20 Find: h

Answer 1

The height of the trapezoid is $h=11.2$

Explanation:

AKLM is a trapezoid.

The measurements of the trapezoid are AK=13, LM=14, KL=5, AM=20

We need to find the height of the trapezoid.

Let M' be a point on AM that is 5 units toward point A from M.

Let B be a point on AM such that KB⊥AM. Let x = AB; then BM' = 15 -x.

Using Pythagorean theorem, we have,

$x^{2}+h^{2}=13^{2}$ --------(1)

$(15-x)^{2}+h^{2}=14^{2}$

$225-30x+x^{2} +h^{2}=14^{2}$-----------(2)

Subtracting the two equations, we have,

$\left(225-30 x+x^{2}+h^{2}\right)-\left(x^{2}+h^{2}\right)=196-169$

Simplifying, we get,

$225-30x=27$

Subtracting both sides of the equation by 225, we get,

$30x=198$

Dividing by 30, we get,

$x=6.6$

Substituting $x=6.6$ in the equation $x^{2}+h^{2}=13^{2}$, we get,

$(6.6)^{2}+h^{2}=169$

$43.56+h^2=169$

             $h=\sqrt{125.44}$

             $h=11.2$

Thus, the height of the trapezoid is $h=11.2$