You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Determinant

The quadrilat...

Question

The quadrilateral formed by the lines y=ax+c, y=ax+d, y=bx+c and y=bx+d has area 18. The quadrilateral formed by the lines y=ax+c, y=ax-d, y=bx+c and y=bx-d has area 72. Ifa,b,c,d are positive integers then the least possible value of the sum a+b+c+d is

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D 16
$\frac{(c - d)^{2}}{| a - b |} = 18$ and $\frac{(c + d)^{2}}{| a - b |} = 72.$
$a = 3, b = 1, d = 3, c = 9$ is a solution for which the minimum is attained.

Suggest Corrections

Similar questions

The quadrilateral formed by the lines y = ax + c, y = ax + d, y = bx + c and y = bx + d has area 18. The quadrilateral formed by the line y = ax + c, y = ax – d, y = ax – d, y = bx + c and y = bx – d has area 72. If a, b, c, d are positive integers then the least possible value of the sum a + b + c + d is

Q. For

a, b, c, d \in N

, the area of the parallelogram bounded by the lines

y = a x + c, y = a x + d, y = b x + c

and

y = b x + d

18

while the area of the parallelogram bounded by the lines

y = a x + c, y = a x - d, y = b x + c

and

y = b x - d

72

. The least possible value of

a + b + c + d

will be:

Equation of line parallel to the line Ax + By + C = 0 is:

Q. if

y^{2} = a x + b x + c

, then

y^{3} \frac{d^{2} y}{d x^{2}}

Q. Match the following provided that

a

and

b

any two rational numbers different from zero and

x, y

are any two rational numbers.

$(1)$	$a^{x} \times a^{y}$	$(a)$	$a^{x - y}$
$(2)$	$a^{x} \div a^{y}$	$(b)$	$a^{x y}$
$(3)$	$(a^{x})^{y}$	$(c)$	$a^{x + y}$
$(4)$	$(a b)^{x}$	$(d)$	$\frac{a^{x}}{b^{x}}$
$(5)$	${(\frac{a}{b})}^{x}$	$(e)$	$a^{x} \times b^{x}$

Join BYJU'S Learning Program

The quadrilateral formed by the lines y=ax+c, y=ax+d, y=bx+c and y=bx+d has area 18. The quadrilateral formed by the lines y=ax+c, y=ax-d, y=bx+c and y=bx-d has area 72. Ifa,b,c,d are positive integers then the least possible value of the sum a+b+c+d is

The correct option is D 16(c−d)2|a−b|=18 and (c+d)2|a−b|=72. a=3,b=1,d=3,c=9 is a solution for which the minimum is attained.

The correct option is D 16
$\frac{(c - d)^{2}}{| a - b |} = 18$ and $\frac{(c + d)^{2}}{| a - b |} = 72.$
$a = 3, b = 1, d = 3, c = 9$ is a solution for which the minimum is attained.