find each measure using the rectangle below to help you.

2. $ad = 7.5\text{ cm}$ and $dc = 10\text{ cm}$. find $db$.

3. $ab = 17\text{ cm}$ and $bc = 12.75\text{ cm}$. find $db$.

Question

find each measure using the rectangle below to help you.

2. $ad = 7.5\text{ cm}$ and $dc = 10\text{ cm}$. find $db$.

3. $ab = 17\text{ cm}$ and $bc = 12.75\text{ cm}$. find $db$.

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Properties of Rectangles", "Pythagorean Theorem" ], "new_concepts": [], "current_concepts": [ "Properties of Rectangles", "Pythagorean Theorem" ] } ## Identify the properties of the rectangle Using the **Properties of Rectangles** knowledge point $$ \begin{aligned} &\angle ADC = 90^\circ\ &\triangle ADC \text{ is a right triangle with hypotenuse } AC\ &AC = DB \text{ (diagonals of a rectangle are equal)} \end{aligned} $$ ## Solve Question 2 Using the **Pythagorean Theorem** knowledge point $$ \begin{aligned} &AC^2 = AD^2 + DC^2\ &AC^2 = 7.5^2 + 10^2 = 56.25 + 100 = 156.25\ &AC = \sqrt{156.25} = 12.5\text{ cm}\ &DB = AC = 12.5\text{ cm} \end{aligned} $$ ## Solve Question 3 Using the **Properties of Rectangles** and **Pythagorean Theorem** knowledge points $$ \begin{aligned} &AD = BC = 12.75\text{ cm (opposite sides are equal)}\ &AC^2 = AD^2 + CD^2 \text{ where } CD = AB = 17\text{ cm}\ &AC^2 = 12.75^2 + 17^2 = 162.5625 + 289 = 451.5625\ &AC = \sqrt{451.5625} = 21.25\text{ cm}\ &DB = AC = 21.25\text{ cm} \end{aligned} $$ ## Question 2 $DB = 12.5\text{ cm}$ ## Question 3 $DB = 21.25\text{ cm}$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Properties of Rectangles" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the properties of the rectangle

Solve Question 2

Solve Question 3

Answer:

Question 2

Question 3