The lengths of the sides and the diagonal of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the parallel sides of the isosceles trapezium be $a$ and $b$,and the non-parallel sides be $c$. Since it is an isosceles trapezium,the non-par

Vedclass · Accepted Answer

$\frac{1}{2}(\sqrt{5}+1)$

Vedclass · Answer

(A) Let the parallel sides of the isosceles trapezium be $a$ and $b$,and the non-parallel sides be $c$. Since it is an isosceles trapezium,the non-parallel sides are equal. The diagonal is $d$. The set of lengths is $\{a, b, c, d\} = \{a, b\}$.Since $a > b$,the sides must be $a, b, a, a$ and the diagonal $d = a$ or $d = b$.Case $1$: The sides are $a, a, a, b$ and the diagonal is $a$. In an isosceles trapezium with parallel sides $a$ and $b$ and non-parallel sides $a$,the diagonal $d$ is given by $d^2 = a^2 + ab - a^2 = ab$ (incorrect geometry).Correct approach: For an isosceles trapezium with parallel sides $a, b$ and non-parallel sides $c$,the diagonal $d$ satisfies $d^2 = c^2 + ab$. Given the set is $\{a, b\}$,we have $c=a$ and $d=a$. Thus $a^2 = a^2 + ab$ is impossible.If $c=b$ and $d=a$,then $a^2 = b^2 + ab$. Dividing by $b^2$,we get $(a/b)^2 - (a/b) - 1 = 0$. Solving for $x = a/b$,$x = \frac{1 + \sqrt{5}}{2}$.

The lengths of the sides and the diagonal of an isosceles trapezium form a two-element set $\{a, b\}$. If $a > b$,then $a / b$ equals

Similar Questions

Let $A = \{a_1, a_2, a_3, \dots, a_n\}$ be a set containing $n$ elements. Two subsets $P$ and $Q$ of $A$ are formed independently. The number of ways in which these subsets can be formed such that $(P - Q)$ contains exactly $2$ elements is:

$A$ number $n$ is chosen at random from $S=\{1, 2, 3, \ldots, 50\}$. Let $A=\{n \in S: n+\frac{50}{n} > 27\}$, $B=\{n \in S: n \text{ is a prime}\}$ and $C=\{n \in S: n \text{ is a square}\}$. Then, the correct order of their probabilities is:

Let $E$ denote the set of letters of the English alphabet,$V = \{a, e, i, o, u\}$ and $C$ be the complement of $V$ in $E$. Then,the number of four-letter words (where repetitions of letters are allowed) having at least one letter from $V$ and at least one letter from $C$ is

Let $A = \{n \in N : n \text{ is a } 3 \text{-digit number}\}$. Let $B = \{9k + 2 : k \in N\}$ and $C = \{9k + l : k \in N\}$ for some $l$ $(0 < l < 9)$. If the sum of all the elements of the set $A \cap (B \cup C)$ is $274 \times 400$,then $l$ is equal to:

The number of $4$-digit numbers that are less than or equal to $2800$ and are either divisible by $3$ or by $11$ is equal to $............$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module