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

## Question 3

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

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

## Question 4

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

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

## Question 5

Find the value of $x$. Calculator recommended

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

## Question 6

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

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

## Question 7

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

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

## Question 8

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

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

## Question 14

Find the perimeter of the following shapes

a) a s v
b) a s v

## Question 15

Find the length of the diagonal in the following cuboids

a) a s v
b) 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