Geometry - Pythagoras Theorem

  a - answer    s - solution    v - video    d - discussion

Question 1


The hypotenuse is the side opposite the right angle
Which letter represents the hypotenuse in these triangles?

a) Pythagorasa s v d
b) Pythagorasa s v d
c) Pythagorasa s v d
d) Pythagorasa s v d
e) Pythagorasa s v d
f) Pythagorasa s v d


Question 2


The square of the hypotenuse is equal to the sum of the squares of the other two sides
Find the area of the shaded square

a) Pythagoras Theorema s v d
b) Pythagoras Theorema s v d
c) Pythagoras Theorema s v d
d) Pythagoras Theorema s v d
e) Pythagoras Theorema s v d
f) Pythagoras Theorema s v d


Question 3


$a^2+b^2=c^2$
Find the value of $x$

a) Pythagorean Theorema s v d
b) Pythagorean Theorema s v d
c) Pythagorean Theorema s v d
d) Pythagorean Theorema s v d
e) Pythagorean Theorema s v d
f) Pythagorean Theorema s v d


Question 4


Find the value of $x$. Leave your answer as a square root

a) Pythagoras Questionsa s v d
b) Pythagoras Questionsa s v d
c) Pythagoras Questionsa s v d
d) Pythagoras Questionsa s v d
e) Pythagoras Questionsa s v d
f) Pythagoras Questionsa s v d


Question 5


Find the value of $x$. Calculator recommended

a) Pythagoras Theorem Questionsa s v d
b) Pythagoras Theorem Questionsa s v d
c) Pythagoras Theorem Questionsa s v d
d) Pythagoras Theorem Questionsa s v d
e) Pythagoras Theorem Questionsa s v d
f) Pythagoras Theorem Questionsa s v d


Question 6


Find the value of $x$. Calculator needed. Leave your answer rounded to one decimal place.

a) Pythagorean Theorem Questionsa s v d
b) Pythagorean Theorem Questionsa s v d
c) Pythagorean Theorem Questionsa s v d
d) Pythagorean Theorem Questionsa s v d
e) Pythagorean Theorem Questionsa s v d
f) Pythagorean Theorem Questionsa s v d


Question 7


Find the value of $x$ by finding Pythagorean Triples/Triads. No calculator

a) Pythagoras Hypothenusea s v d
b) Pythagoras Hypothenusea s v d
c) Pythagoras Hypothenusea s v d
d) Pythagoras Hypothenusea s v d
e) Pythagoras Hypothenusea s v d
f) Pythagoras Hypothenusea s v d


Question 8


Find the value of $x$. Calculator needed. Leave your answer rounded to two decimal places.

a) Pythagoras Theorem Hypothenusea s v d
b) Pythagoras Theorem Hypothenusea s v d
c) Pythagoras Theorem Hypothenusea s v d
d) Pythagoras Theorem Hypothenusea s v d
e) Pythagoras Theorem Hypothenusea s v d
f) Pythagoras Theorem Hypothenusea s v d


Question 9


Find the value of $x$ so that the following three terms form a Pythagorean Triple/Triad. No calculator

a) $3,4,x$a s v d
b) $5,12,x$a s v d
c) $8,15,x$a s v d
d) $0.05,0.12,x$a s v d
e) $8\,000,15\,000,x$a s v d
f) $15,20,x$a s v d
g) $\frac{5}{23},\frac{12}{23},x$a s v d
h) $\frac34,1,x$a s v d
i) $9,40,x$a s v d
j) $88,165,x$a s v d
k) $\frac25,\frac34,x$a s v d
l) $\frac32,\frac{36}{7},x$a s v d


Question 10


Find the value of $x$ so that the following three terms form a Pythagorean Triple/Triad. Leave your answer as a square root

a) $6,11,x$a s v d
b) $9,20,x$a s v d
c) $12,13,x$a s v d
d) $1,5,x$a s v d
e) $1,1,x$a s v d
f) $13,14,x$a s v d


Question 11


Find the value of $x$ so that the following three terms form a Pythagorean Triple/Triad. Calculator required. Round your answer to three significant figures

a) $4,7,x$a s v d
b) $8,8,x$a s v d
c) $9,15,x$a s v d
d) $18,26,x$a s v d
e) $27,51,x$a s v d
f) $111,135,x$a s v d


Question 12


Find the value of $x$ so that the following three terms form a Pythagorean Triple/Triad. Knowledge of solving linear equations needed. *Knowledge of solving quadratic equations needed

a) $3,4,x-1$a s v d
b) $x,12,x+8$a s v d
c) $x+11,15,x+20$a s v d
d) $15,2x,2x+5$a s v d
e) *$x+2,x+3,x+4$a s v d
f) *$18-x,3x,4x-6$a s v d


Question 13


Find the pronumerals

a) Pythagorasa s v d
b) Pythagoras Theorema s v d
c) Pythagorean Theorema s v d
d) Pythagoras Questiona s v d
e) Pythagoras Theorem Questiona s v d
f) Pythagorean Theorem Questiona s v d


Question 14


Find the perimeter of the following shapes

a) Pythagoras Perimetera s v d
b) Pythagoras Theorem Perimetera s v d


Question 15


Find the length of the diagonal in the following cuboids

a) Pythagoras 3Da s v d
b) Pythagoras Theorem 3Da s v d


Question 16


The dimensions for a cuboid are given (length, width and height). Find the length of the space diagonal. Calculator may be needed

a) $3,4,12$a s v d
b) $8,9,12$a s v d
c) $12,21,28$a s v d
d) $9,24,32$a s v d
e) $5,12,84$a s v d
f) $28,75,180$a s v d