Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

EFGHEFGH is a rhombus. Given EG=16EG=16 and FH=12FH=12, what is the length of one side of the rhombus?\newline66 units\newline88 units\newline1010 units\newline1414 units

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right chevron icon
Evaluate radical expressionsright chevron icon

Full solution

Q. EFGHEFGH is a rhombus. Given EG=16EG=16 and FH=12FH=12, what is the length of one side of the rhombus?\newline66 units\newline88 units\newline1010 units\newline1414 units
  1. Form Right-Angled Triangles: A rhombus has diagonals that bisect each other at right angles. To find the length of one side of the rhombus, we can use the diagonals to form right-angled triangles. Each triangle will have half the length of each diagonal as its legs.\newlineCalculation: Half of EG=162=8EG = \frac{16}{2} = 8 units, Half of FH=122=6FH = \frac{12}{2} = 6 units
  2. Use Pythagorean Theorem: Using the Pythagorean theorem for one of the right-angled triangles formed by the diagonals, we can find the length of one side of the rhombus (which is the hypotenuse of the triangle). The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse cc is equal to the sum of the squares of the other two sides aa and bb.
    Calculation: c2=a2+b2c^2 = a^2 + b^2, where cc is the length of one side of the rhombus, aa is half of EG, and bb is half of FH.
  3. Substitute Values: Substitute the values of aa and bb into the Pythagorean theorem to find c2c^2.\newlineCalculation: c2=82+62=64+36=100c^2 = 8^2 + 6^2 = 64 + 36 = 100
  4. Find Length of Side: Find the value of cc by taking the square root of c2c^2.\newlineCalculation: c=100=10c = \sqrt{100} = 10 units

More problems from Evaluate radical expressions

Question
Evaluate the expression for j=7 j = 7 .\newline2j= 2j = _____
Get tutor helpright-arrow

Posted 3 months ago

Question
Evaluate the expression for y=4 y = 4 and z=5 z = 5 . \newline yz= yz = _____
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate the expression for t=0 t = 0 .\newline∣−4−t∣=|-4 - t| = _____
Get tutor helpright-arrow

Posted 3 months ago

Question
Dale drew 88 pictures. Belle drew pp fewer pictures than Dale. Choose the expression that shows how many pictures Belle drew. \newlineChoices: \newline(A) 88\newline(B) p−8p - 8\newline(C) 8+p8 + p\newline(D) 8−p8 - p
Get tutor helpright-arrow

Posted 3 months ago

Question
Write an expression for the sequence of operations described below. subtract 55 from 66, then add ww to the result Do not simplify any part of the expression. ______
Get tutor helpright-arrow

Posted 3 months ago

Question
Write an expression for the operation described below. \newlinesubtract 44 from aa \newline______
Get tutor helpright-arrow

Posted 3 months ago

Question
John baked 1212 cookies. Alice baked nn fewer cookies than John.\newline Choose the expression that shows how many cookies Alice baked.\newline Choices:\newline(A) 1212\newline(B) n−12n - 12\newline(C) 12+n12 + n\newline(D) 12−n12 - n
Get tutor helpright-arrow

Posted 4 months ago

Question
Emma read 1515 books. Lucas read bb fewer books than Emma. Choose the expression that shows how many books Lucas read.\newlineChoices:\newline(A) 1515\newline(B) b−15b - 15\newline(C) 15+b15 + b\newline(D) 15−b15 - b
Get tutor helpright-arrow

Posted 4 months ago

Question
Max ran 1010 miles. Sarah ran mm fewer miles than Max. Choose the expression that shows how many miles Sarah ran.\newlineChoices:\newline(A)10(A)10\newline(B)m−10(B)m - 10\newline(C)10+m(C)10 + m\newline(D)10−m(D)10 - m
Get tutor helpright-arrow

Posted 4 months ago

Question
Carlos wrote 2020 poems. Fiona wrote pp fewer poems than Carlos. Choose the expression that shows how many poems Fiona wrote.\newlineChoices:\newline(A) 2020\newline(B) p−20p - 20\newline(C) 20+p20 + p\newline(D) 20−p20 - p
Get tutor helpright-arrow

Posted 4 months ago

View all (28)