Question

given rectangle ( ghij ) below, ( hk = 70 ). if ( gi = x - 5 ), solve for ( x ).

Explanation:

Step1: Recall the property of rectangle diagonals

In a rectangle, the diagonals are equal and bisect each other. So \(GI = HJ\) and \(HK=\frac{1}{2}HJ\).
Since \(HK = 70\), then \(HJ=2\times HK\).

Step2: Calculate the length of \(GI\)

\(HJ = 2\times70=140\). And because \(GI = HJ\) (diagonals of a rectangle are equal), so \(GI=140\).

Step3: Solve for \(x\)

Given \(GI=x - 5\), and \(GI = 140\). Then \(x-5=140\). Add 5 to both sides of the equation: \(x=140 + 5\).

Answer:

\(x = 145\)