Advertisements
Advertisements
Question
The perimeter of a rectangular field is 82 m and its area is 400 m2. Find the breadth of the rectangle.
Advertisements
Solution
Let the breadth of the rectangle be x meters. Then
Perimeter = 82 meters
2(length + breadth) = 82
(length + x) = 41
length = 41 − x
And area of the rectangle
length x bradth = 400
(41 − x) x = 400
41x − x2 = 400
x2 − 41x + 400 = 0
x2 − 25x − 16x + 400 = 0
x(x − 25) −16(x − 25) = 0
(x − 25) (x − 16) = 0
or
x − 16 = 0
x = 16
Since perimeter is 82 meter. So breadth can’t be 25 meter.
Hence, breadth 16 meters.
APPEARS IN
RELATED QUESTIONS
Find the roots of the following quadratic equation by factorisation:
100x2 – 20x + 1 = 0
Find the whole numbers which when decreased by 20 is equal to 69 times the reciprocal of the members.
If \[1 + \sqrt{2}\] is a root of a quadratic equation with rational coefficients, write its other root.
Show that x = –3 is a solution of x2 + 6x + 9 = 0.
If a and b are roots of the equation x2 + ax + b = 0, then a + b =
Solve the following equation:
`("x" + 1)/("x" - 1) - ("x" - 1)/("x" + 1) = 5/6 , "x" ≠ -1,1`
Solve the following equation: a2b2x2 + b2x - a2x - 1 = 0
Let ∆ ABC ∽ ∆ DEF and their areas be respectively, 64 cm2 and 121 cm2. If EF = 15⋅4 cm, find BC.
Solve the following equation by factorization
x(6x – 1) = 35
Mohini wishes to fit three rods together in the shape of a right triangle. If the hypotenuse is 2 cm longer than the base and 4 cm longer than the shortest side, find the lengths of the rods.
