Advertisements
Advertisements
Question
The sides of triangle is given below. Determine it is right triangle or not.
a = 1.6 cm, b = 3.8 cm and c = 4 cm
Solution
In order to prove that the given sides of a certain triangle forms a right angled triangle we have to prove that square of the larger side is equal to the sum of the squares of the other two sides.
Here, the larger side is c = 4 cm.
Hence, we have to prove that a2 + b2 = c2..
Let solve the left hand side of the above equation.
a2 + b2 = (1.6)2 + (3.8)2
= 2.56 + 14.44
= 17
Now we will solve the right hand side of the equation,
c2 = 42 = 16
Here we can observe that left hand side is not equal to the right hand side.
Therefore, the given sides of a certain triangle do not form a right angled triangle.
APPEARS IN
RELATED QUESTIONS
If the sides of a triangle are 3 cm, 4 cm, and 6 cm long, determine whether the triangle is a right-angled triangle.
Two poles of height 9 m and 14 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.
A triangle has sides 5 cm, 12 cm and 13 cm. Find the length to one decimal place, of the perpendicular from the opposite vertex to the side whose length is 13 cm.
In a ΔABC, AB = BC = CA = 2a and AD ⊥ BC. Prove that
(i) AD = a`sqrt3`
(ii) Area (ΔABC) = `sqrt3` a2
Calculate the height of an equilateral triangle each of whose sides measures 12 cm.
In an equilateral ΔABC, AD ⊥ BC, prove that AD2 = 3BD2.
A man goes 12m due south and then 35m due west. How far is he from the starting point.
The co-ordinates of the points A, B and C are (6, 3), (−3, 5) and (4, −2) respectively. P(x, y) is any point in the plane. Show that \[\frac{ar\left( ∆ PBC \right)}{ar\left( ∆ ABC \right)} = \left| \frac{x + y - 2}{7} \right|\]
From given figure, In ∆ABC, AB ⊥ BC, AB = BC, AC = `5sqrt(2)` , then what is the height of ∆ABC?
Find the height of an equilateral triangle having side 4 cm?
