Information
You have already completed the quiz before. Hence you can not start it again.
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
-
Question 1 of 4
ABCD is a square with BD=18 cm. Find the length of AB.
Round your answer to 2 decimal places
Incorrect
Loaded: 0%
Progress: 0%
0:00
Method One
Finding a Side
Use -
a2=c2-b2
Labelling each length of the triangle
All sides of a square are equal, so a=b=AB.
Use the formula for Finding a Side to solve for AB
a2 |
= |
c2−b2 |
Finding a Side |
AB2 |
= |
182−AB2 |
Plug in the known lengths |
AB2 +AB2 |
= |
324−AB2 +AB2 |
Add AB2 to both sides |
2AB2 |
= |
324 |
AB2−AB2 cancels out |
2AB2÷2 |
= |
324÷2 |
Divide both sides by 2 |
2AB2÷2 |
= |
162 |
×2÷2 cancels out |
√AB2 |
= |
√162 |
Take the square root of both sides |
AB |
= |
12.73 cm |
Rounded to two decimal places |
Method Two
Labelling each length of the triangle
All sides of a square are equal, so a=b=AB.
We can use the Pythagorean Theorem Formula to solve for AB
a2+b2 |
= |
c2 |
Pythagoras’ Theorem Formula |
AB2+AB2 |
= |
182 |
Plug in the known lengths |
2AB2 |
= |
324 |
Evaluate |
2AB2÷2 |
= |
324÷2 |
Divide both sides by 2 |
2AB2÷2 |
= |
162 |
×2÷2 cancels out |
√AB2 |
= |
√162 |
Take the square root of both sides |
AB |
= |
12.73 cm |
Rounded to two decimal places |
-
Question 2 of 4
Find the value of the missing length
The given measurements are in units
Round your answer to one decimal place
Incorrect
Method One
Finding a Side
Use -
b2=c2-a2
Labelling each length of the triangle
Use the formula for Finding a Side to solve for b
b2 |
= |
c2−a2 |
Finding a Side |
b2 |
= |
10.62−2.92 |
Plug in the known lengths |
b2 |
= |
112.36−8.41 |
Evaluate |
b2 |
= |
103.95 |
√b2 |
= |
√103.95 |
Take the square root of both sides |
b |
= |
10.2 units |
Rounded to one decimal place |
Method Two
Labelling each length of the triangle
Use the Pythagorean Theorem Formula to solve for b
a2+b2 |
= |
c2 |
Pythagoras’ Theorem Formula |
2.92+b2 |
= |
10.62 |
Plug in the known lengths |
8.41+b2 |
= |
112.36 |
Evaluate |
8.41+b2 −8.41 |
= |
112.36 −8.41 |
Subtract 8.41 from both sides |
8.41+b2 −8.41 |
= |
103.95 |
8.41−8.41 cancels out |
√b2 |
= |
√103.95 |
Take the square root of both sides |
b |
= |
10.2 units |
Rounded to one decimal place |
-
Question 3 of 4
The foot of a ladder is 3 metres from the base of a brick wall. If the ladder reaches 7 metres up the wall, find its length.
Round your answer to a whole number
Incorrect
Loaded: 0%
Progress: 0%
0:00
Labelling each length of the triangle
Use the Pythagorean Theorem Formula to solve for c
a2+b2 |
= |
c2 |
Pythagoras’ Theorem Formula |
32+72 |
= |
x2 |
Plug in the known lengths |
9+49 |
= |
x2 |
Evaluate |
√x2 |
= |
√58 |
Take the square root of both sides |
x |
= |
8 m |
Rounded to the nearest metre |
-
Question 4 of 4
Find the value of the missing length b
a=23.5 b=? c=32.4
The given measurements are in units
Round your answer to one decimal place
Incorrect
Method One
Finding a Side
Use -
b2=c2-a2
Labelling each length of the triangle
a=23.5
c=32.4
Use the formula for Finding a Side to solve for b
b2 |
= |
c2−a2 |
Finding a Side |
b2 |
= |
32.42−23.52 |
Plug in the known lengths |
b2 |
= |
1049.76−552.25 |
Evaluate |
b2 |
= |
497.51 |
√b2 |
= |
√497.51 |
Take the square root of both sides |
b |
= |
22.3 units |
Rounded to one decimal place |
Method Two
Labelling each length of the triangle
a=23.5
c=32.4
Use the Pythagorean Theorem Formula to solve for b
a2+b2 |
= |
c2 |
Pythagoras’ Theorem Formula |
23.52+b2 |
= |
32.42 |
Plug in the known lengths |
552.25+b2 |
= |
1049.76 |
Evaluate |
552.25+b2 −552.25 |
= |
1049.76 −552.25 |
Subtract 552.25 from both sides |
552.25+b2 −552.25 |
= |
497.51 |
552.25−552.25 cancels out |
√b2 |
= |
√497.51 |
Take the square root of both sides |
b |
= |
22.3 units |
Rounded to one decimal place |