Question
The sides of certain triangles are given below. Determine them are right triangles:
$9\ cm, 16\ cm, 18\ cm.$
$9\ cm, 16\ cm, 18\ cm.$
✓
Answer
For a given triangle to be a right angled, the sum of the squares of the two sides must be equal to the square of the largest side.
Let $a = 9\ cm, b = 16\ cm$ and$ c= 18\ cm.$ Then
$\Big(\text{a}^2+\text{b}^2\Big)=\Big[9^2+(16)^2\Big]$
$=(81+256)\text{cm}^2$
$=337\text{cm}^2$
and $\text{c}^2=(18)^2\text{cm}^2=324\text{cm}^2$
$\therefore\big(\text{a}^2+\text{b}^2\big)\not=\text{c}^2$
Hence the given triangle is not right angled.
Let $a = 9\ cm, b = 16\ cm$ and$ c= 18\ cm.$ Then
$\Big(\text{a}^2+\text{b}^2\Big)=\Big[9^2+(16)^2\Big]$
$=(81+256)\text{cm}^2$
$=337\text{cm}^2$
and $\text{c}^2=(18)^2\text{cm}^2=324\text{cm}^2$
$\therefore\big(\text{a}^2+\text{b}^2\big)\not=\text{c}^2$
Hence the given triangle is not right angled.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
An AP consists of $50$ terms of which $3^{rd}$ term is $12$ and the last term is $106$. Find the $29^{th}$ term.
→In the given figure, there are two concentric circles with centre $O$ of radii 5cm and 3cm. From an external point $P,$ tangent $PA$ and $PB$ are drawn to these circles.
If $AP = 12\ cm,$ find the length of $BP.$
→If $AP = 12\ cm,$ find the length of $BP.$
The rain water from a roof of dimensions $22\ m × 20\ m$ drains into a cylindrical vessel having diameter of base $2\ m $ and height $3.5\ m.$ If the rain water collected from the roof just fills the cylindrical vessel, then find the rain in cm.
→State Pythagoras theorem and its converse.
Prove that following numbers are irrationals:
$4+\sqrt{2}$
→$4+\sqrt{2}$
Two cubes each of volume $27cm^3$ are joined end to end to form a solid. Find the surface area of the resulting cuboid.
→Find the sum of,
All $2$ - digit natural numbers divisible by $4.$
→All $2$ - digit natural numbers divisible by $4.$
Find the number of terms of the $A.P. -12, -9, -6, ....., 21.$ If 1 is added to each term of this $A.P.,$ then find the sum of all terms of the $A.P.$ thus obtained.
→Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of $\triangle$PQR (see figure). Show that $\triangle A B C \sim \triangle P Q R$.
→In the given figure, $\angle\text{CAB}=90^\circ$ and $\text{AD}\perp\text{BC}.$ Show that $\triangle\text{BDA}\sim\triangle\text{BAC}.$ If $AC = 75\ cm, AB = 1m,$ and $BC = 1,25m$ find $AD.$
→