Question

if ( eh = 4w - 28 ) and ( gh = 2w ), find ( eh ) in rectangle ( defg ).

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, the diagonals bisect each other. So \(EH = GH\).
$$4w - 28=2w$$

Step2: Solve the equation for \(w\)

Subtract \(2w\) from both sides:
$$4w-2w - 28=2w-2w$$
$$2w-28 = 0$$
Add \(28\) to both sides:
$$2w-28 + 28=0 + 28$$
$$2w=28$$
Divide both sides by \(2\):
$$w=\frac{28}{2}=14$$

Step3: Find the value of \(EH\)

Substitute \(w = 14\) into \(EH=4w - 28\):
$$EH=4\times14-28$$
$$EH = 56 - 28$$
$$EH=28$$

Answer:

\(28\)