Question

qr is a midsegment of triangle fgh. solve for the value of x?

Explanation:

Step1: Apply the midsegment theorem

The midsegment theorem states that the length of the midsegment of a triangle is half the length of the base. So, \(2(x + 22)=x + 33\).

Step2: Expand the left - hand side

Using the distributive property \(a(b + c)=ab+ac\), we get \(2x+44=x + 33\).

Step3: Solve for \(x\)

Subtract \(x\) from both sides: \(2x - x+44=x - x+33\), which simplifies to \(x+44 = 33\). Then subtract 44 from both sides: \(x+44-44=33 - 44\), so \(x=-11\).

Answer:

-11