HIJK is a rectangle. Find the value of x and the length of each diagonal ### Problem 13**Rectangle HIJK***Find the value of \( x \) and the length of each diagonal if \( HJ = 3x^3 - 7x - 4 \) and \( IK = x^2 - 6x - 1 \).*- **Diagram:** The rectangle is labeled as HIJK with \( H \) at the top left, \( I \) at the top right, \( K \) at the bottom left, and \( J \) at the bottom right.- **Equations:** - \( x = \) __________ - \( HJ = \) __________ - \( IK = \) __________### Problem 14*Find the perimeter and area of each figure. Give EXACT answers in simplest radical form, if needed.*- **Diagram:** A square with a diagonal and one side marked as 7 inches.- **Measurements:** - **Side length =** __________ - **Perimeter =** __________ - **Area =** __________ **Worksheet on Geometry: Rhombus and Rectangle Problems**### Part A: RhombusGiven that **ABCD is a rhombus**, the following measures need to be found. Also, state the theorem or definition that supports each statement:1. **AB = ___________** - **Why?** (Statement and explanation needed)2. **m∠ABC = ___________** - **Why?** (Statement and explanation needed)*Diagram Description:* In the diagram, quadrilateral ABCD is labeled with lines and equations assigned to its sides and angles. Angles and sides are represented using algebraic expressions, for instance, *4x + 15* and *(xy - 1)°*. ### Part B: RectangleRectangle **HIJK** Problem:- **Objective**: Find the value of x and the length of each diagonal.- If **HJ = 3x² - 7x - 4** and **IK = x² - 6x - 1**, solve for the following: - **x = ___________** - **HJ = ___________** - **IK = ___________***Diagram Description:* A rectangle labeled as HIJK is shown. The task requires using given quadratic equations representing the diagonals to solve for specific values.**Instructions:**- Provide exact answers in simplest radical form, if necessary.- Use applicable geometric theorems and definitions to justify your solutions.

Name: HIJK is a rectangle. Find the value of x and the length of each diagon
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: HIJK is a rectangle. Find the value of x and the length of each diagonal ### Problem 13**Rectangle HIJK***Find the value of \( x \) and the length of each diagonal if \( HJ = 3x^3 - 7x - 4 \) and \( IK = x^2 - 6x - 1 \).*- **Diagram:** The rectangle