Question : The length of the sides of a triangle is $a, b,$ and $c$ respectively if $a^2 + b^2 + c^ 2 = ab + bc + ca$, then the triangle is:
Option 1: Isosceles
Option 2: Equilateral
Option 3: Scalene
Option 4: Right-angled
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: Equilateral
Solution : Given: $a^2 + b^2 + c^2 = ab + bc + ca$ Multiplying both sides by 2, $⇒2(a^2 + b^2 + c^2) = 2(ab + bc + ca)$ $⇒a^2 - 2ab + b^2 + b^2 - 2bc + c^2 + c^2 - 2ca + a^2 = 0$ $⇒(a-b)^2 + (b-c)^2 + (c-a)^2 = 0$. Since the sum of squares is zero, each term must be zero, which implies that $a=b$, $b=c$, and $c=a$. Therefore, the triangle is equilateral because all its sides are equal. Hence, the correct answer is Equilateral.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : If one angle of a triangle is equal to half the sum of the other two equal angles, then the triangle is:
Question : x, y, and z are the sides of a triangle. If z is the largest side and x2 + y2 > z2, then the triangle is a:
Question : In a triangle, if three altitudes are equal, then the triangle is:
Question : If $\frac{a^{2} - bc}{a^{2}+bc}+\frac{b^{2}-ca}{b^{2}+ca}+\frac{c^{2}-ab}{c^{2}+ab}=1$, then the value of $\frac{a^{2}}{a^{2}+bc}+\frac{b^{2}}{b^{2}+ac}+\frac{c^{2}}{c^{2}+ab}$ is:
Question : If in acute-angled triangle ABC, AL, BM, and CN are the three altitudes of triangle ABC, then which of the following statements will be true?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile