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Geometry - Pythagoras Theorem

  a - answer    s - solution    v - video

Question 1


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

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


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


Question 3


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

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


Question 4


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

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


Question 5


Find the value of $x$. Calculator recommended

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


Question 6


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

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


Question 7


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

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


Question 8


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

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


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


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


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


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


Question 13


Find the pronumerals

a) Pythagoras  a s v
b) Pythagoras Theorem  a s v
c) Pythagorean Theorem  a s v
d) Pythagoras Question  a s v
e) Pythagoras Theorem Question  a s v
f) Pythagorean Theorem Question  a s v


Question 14


Find the perimeter of the following shapes

a) Pythagoras Perimeter  a s v
b) Pythagoras Theorem Perimeter  a s v


Question 15


Find the length of the diagonal in the following cuboids

a) Pythagoras 3D  a s v
b) Pythagoras Theorem 3D  a s v


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