Let the three sides of a trapezium are equal and each equal to 6 cm . If area of trapezium is maximum, then length of fourth side of trapezium is

Question

Let the three sides of a trapezium are equal and each equal to 6 cm . If area of trapezium is maximum, then length of fourth side of trapezium is (A) 6 cm (B) 9 cm (C) 12 cm (D) 15 cm

Tardigrade Admin · Accepted Answer

Ar=(1/2)(.12+2x.)⋅ √36 - x2 (d A/d x)=1⋅ √36 - x2+((. 6 + x .) (. - 2 x .)/2 √36 - x2)=0 <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-s9o3j5vfrvafwqjj.jpg" /> ⇒ 36-x2-x2-6x=0 ⇒ x2+3x-18=0 ⇒ (.x+6.)(.x-3.)=0 ⇒ x=3

Q. Let the three sides of a trapezium are equal and each equal to $6 c m$ . If area of trapezium is maximum, then length of fourth side of trapezium is

$6 c m$

$9 c m$

$12 c m$

$15 c m$

$A r = \frac{1}{2} (12 + 2 x) \cdot 36 - x^{2}$
$\frac{d A}{d x} = 1 \cdot 36 - x^{2} + \frac{( 6 + x ) ( - 2 x )}{2 36 - x ^{2}} = 0$

$\Rightarrow 36 - x^{2} - x^{2} - 6 x = 0$
$\Rightarrow x^{2} + 3 x - 18 = 0$
$\Rightarrow (x + 6) (x - 3) = 0$
$\Rightarrow x = 3$

Q. Let the three sides of a trapezium are equal and each equal to 6cm . If area of trapezium is maximum, then length of fourth side of trapezium is

6cm

9cm

12cm

15cm