Question

if $uv = t - 85$ and $wy = t - 87$, what is the value of $t$? image of a geometric figure with segments marked as equal

Explanation:

Step1: Apply the mid - segment theorem

In a triangle, the mid - segment (a segment connecting the midpoints of two sides of a triangle) is half the length of the third side. Here, \(WY\) is a mid - segment and \(UV\) is the third side. So, \(UV = 2\times WY\).

Step2: Substitute the given expressions

Given \(UV=t - 85\) and \(WY=t - 87\), substitute into \(UV = 2\times WY\). We get \(t-85 = 2(t - 87)\).

Step3: Expand the right - hand side

Using the distributive property \(a(b + c)=ab+ac\), \(2(t - 87)=2t-174\). So the equation becomes \(t - 85=2t-174\).

Step4: Solve for \(t\)

Subtract \(t\) from both sides: \((t - 85)-t=(2t-174)-t\). This simplifies to \(- 85=t - 174\). Then add \(174\) to both sides: \(-85 + 174=t-174 + 174\).

Answer:

\(t = 89\)