Advertisements
Advertisements
Question
The sides of the triangle are given below. Find out which one is the right-angled triangle?
1.5, 1.6, 1.7
Advertisements
Solution
It is known that, if in a triplet of natural numbers, the square of the biggest number is equal to the sum of the squares of the other two numbers, then the three numbers form a Pythagorean triplet. If the lengths of the sides of a triangle form such a triplet, then the triangle is a right-angled triangle.
The sides of the given triangle are 1.5, 1.6, and 1.7.
Let us check whether the given set (1.5, 1.6, 1.7) forms a Pythagorean triplet or not.
The biggest number among the given set is 1.7.
(1.7)2 = 2.89; (1.5)2 = 2.25; (1.6)2 = 2.56
Now, 2.25 + 2.56 = 4.81 ≠ 2.89
∴ (1.5)2 + (1.6)2 ≠ (1.7)2
Thus, (1.5, 1.6, 1.7) does not form a Pythagorean triplet.
Hence, the given triangle with sides 1.5, 1.6, and 1.7 is not a right-angled triangle.
RELATED QUESTIONS
ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, prove that ABC is a right triangle.
Prove that the points A(0, −1), B(−2, 3), C(6, 7) and D(8, 3) are the vertices of a rectangle ABCD?
In the figure: ∠PSQ = 90o, PQ = 10 cm, QS = 6 cm and RQ = 9 cm. Calculate the length of PR.
O is any point inside a rectangle ABCD.
Prove that: OB2 + OD2 = OC2 + OA2.
Triangle XYZ is right-angled at vertex Z. Calculate the length of YZ, if XY = 13 cm and XZ = 12 cm.
In ΔABC, AD is perpendicular to BC. Prove that: AB2 + CD2 = AC2 + BD2
In a right-angled triangle ABC,ABC = 90°, AC = 10 cm, BC = 6 cm and BC produced to D such CD = 9 cm. Find the length of AD.
Find the distance between the helicopter and the ship
For going to a city B from city A, there is a route via city C such that AC ⊥ CB, AC = 2x km and CB = 2(x + 7) km. It is proposed to construct a 26 km highway which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction of the highway.
Two circles having same circumference are congruent.
