Question

solve for x. (just put the number, not x = !!!!)
your answer
the figure shown below is a square. solve for x. (just put the number, not x = !!!!)

Explanation:

Step1: Identify the property of the rectangle

In a rectangle, the diagonals are equal in length and bisect each other, but here we use the fact that \(\angle QRS = 90^{\circ}\). So \((2x + 1)+(7x - 37)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+7x+1 - 37=90\), which gives \(9x-36 = 90\).

Step3: Isolate the term with \(x\)

Add 36 to both sides: \(9x=90 + 36\), so \(9x=126\).

Step4: Solve for \(x\)

Divide both sides by 9: \(x=\frac{126}{9}=14\).

For the square:

Step1: Use the property of the square's diagonal

In a square, the diagonal bisects the vertex angle. The vertex angle of a square is \(90^{\circ}\), and the diagonal bisects it into two \(45^{\circ}\) angles. So \(7x+3 = 45\).

Step2: Solve for \(x\)

Subtract 3 from both sides: \(7x=45 - 3=42\). Then divide both sides by 7: \(x=\frac{42}{7}=6\).

Answer:

14
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