Question

determine whether the figure is a rectangle, rhombus, or square.

rectangle
rhombus
square
fghj is a square. solve for y.

Explanation:

First Sub - Question (Determine the figure type)

A square has four right angles (like a rectangle) and four equal - length sides (like a rhombus). The given figure has right angles (marked by the square symbols) and also has markings indicating that opposite sides are equal and the sides that are marked as equal (the tick marks and arrow marks) suggest that all sides are equal. A rectangle has four right angles but not necessarily four equal sides, and a rhombus has four equal sides but not necessarily four right angles. Since this figure has both four right angles and four equal - length sides, it is a square.

Step 1: Recall the property of a square

In a square, all sides are equal in length. So, the length of side \(FJ\) (which is \(15y + 2\)) and the length of side \(JH\) (which is \(11y+10\)) should be equal. We set up the equation: \(15y + 2=11y + 10\).

Step 2: Solve the equation for \(y\)

Subtract \(11y\) from both sides of the equation: \(15y-11y + 2=11y-11y + 10\), which simplifies to \(4y+2 = 10\).
Then subtract 2 from both sides: \(4y+2 - 2=10 - 2\), so \(4y=8\).
Divide both sides by 4: \(\frac{4y}{4}=\frac{8}{4}\), which gives \(y = 2\).

Answer:

square

Second Sub - Question (Solve for \(y\) in square \(FGHJ\))