A right triangle has hypotenuse $p \ cm$ and one side $q \ cm.$ If $p - q = 1,$ find the length of third side of the triangle.
View full solution →Question types
Pythagoras Theorem question types
33 questions across 3 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.
33
Questions
3
Question groups
5
Question types
Sample Questions
Pythagoras Theorem questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Find the length of the hypotenuse of a triangle whose other two sides are $24\ cm$ and $7\ cm.$
View full solution →In $\triangle A B C$, $A D$ is perpendicular to $B C$. Prove that: $A B^2+C D^2=A C^2+B D^2$
View full solution →Each side of rhombus is $10 \ cm$. If one of its diagonals is $16 \ cm,$ find the length of the other diagonals.
View full solution →The length of the diagonals of rhombus are $24\ cm$ and $10\ cm.$ Find each side of the rhombus.
View full solution →Two poles of height $9\ m$ and $14\ m$ stand on a plane ground. If the distance between their $12\ m$, find the distance between their tops.
View full solution →A ladder $25\ m$ long reaches a window of a building $20\ m$ above the ground. Determine the distance of the foot of the ladder from the building.
View full solution →A man goes $10\ m$ due east and then $24\ m$ due north. Find the distance from the straight point.
View full solution →Calculate the area of a right$-$angled triangle whose hypotenuse is $65\ cm$ and one side is $16\ cm$.
View full solution →$\text{PQR}$ is an isosceles triangle with $PQ = PR = 10 \ cm$ and $QR = 12 \ cm$. Find the length of the perpendicular from $P$ to $QR$.
View full solution →The foot of a ladder is $6\ m$ away from a wall and its top reaches a window $8\ m$ above the ground. If the ladder is shifted in such a way that its foot is $8\ m$ away from the wall to what height does its tip reach?
View full solution →A ladder $15\ m$ long reaches a window which is $9\ m$ above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to other side of the street to reach a window $12\ m$ high. Find the width of the street.
View full solution →In a square $\text{PQRS}$ of side $5\ cm, A, B, C$ and $D$ are points on sides $PQ, QR, RS$ and $SP$ respectively such as $PA = PD = RB = RC = 2\ cm.$ Prove that $\text{ABCD}$ is a rectangle. Also, find the area and perimeter of the rectangle.
View full solution →In a right$-$angled $\triangle P Q R$, right$-$angled at $Q, S$ and $T$ are points on $P Q$ and $Q R$ respectively such as $P T=S R=13\ cm , Q T=5 \ cm$ and $P S=T R$. Find the length of $P Q$ and $P S$.
View full solution →In a right$-$angled $\triangle A B C, A B C=90^{\circ}, A C=10 \ cm, B C=6 \ cm$ and $B C$ produced to $D$ such $C D=9 \ cm$. Find the length of $AD.$
View full solution →Generate a Pythagoras Theorem paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.