Advertisements
Advertisements
प्रश्न
The hypotenuse of grassy land in the shape of a right triangle is 1 metre more than twice the shortest side. If the third side is 7 metres more than the shortest side, find the sides of the grassy land.
उत्तर
Let the shortest side = x
Hypotenuse = 2x + 1
and third side = x + 7
According to the condition,
(2x + 1)2 = x2 + (x + 7)2
⇒ 4x2 + 4x + 1 = x2 + x2 + 14x + 49
⇒ 4x2 + 4x + 1 - 2x2 - 14x - 49 = 0
⇒ 2x2 - 10x - 48 = 0
⇒ x2 - 5x - 24 = 0 ...(Dividing by 2)
⇒ x2 - 8x + 3x - 24 = 0
⇒ x(x - 8) + 3(x - 8) = 0
⇒ (x - 8)(x + 3) = 0
EIther x - 8 = 0,
then x = 8
or
x + 3 = 0,
then x = -3,
but it is not possible as it is negative.
∴ Shortest side = 8m
Third side
= x + 7
= 8 + 7
= 15m
and hypotenuse
= 2x + 1
= 8 x 2 + 1
= 16 + 1
= 17m.
APPEARS IN
संबंधित प्रश्न
Solve for x :
`1/(x + 1) + 3/(5x + 1) = 5/(x + 4), x != -1, -1/5, -4`
Solve the following quadratic equations by factorization:
`x^2+(a+1/a)x+1=0`
The sum of the squares of two numbers as 233 and one of the numbers as 3 less than twice the other number find the numbers.
If x = 1 is a common roots of the equations ax2 + ax + 3 = 0 and x2 + x + b = 0, then ab =
The sum of a number and its reciprocal is `2 9/40`. Find the number.
Find two natural numbers which differ by 3 and whose squares have the sum of 117.
A two digit number is such that the product of the digits is 12. When 36 is added to this number the digits interchange their places. Determine the number.
A shopkeeper purchases a certain number of books for Rs. 960. If the cost per book was Rs. 8 less, the number of books that could be purchased for Rs. 960 would be 4 more. Write an equation, taking the original cost of each book to be Rs. x, and Solve it to find the original cost of the books.
Which of the following are the roots of the quadratic equation, x2 – 9x + 20 = 0 by factorisation?
Find the roots of the following quadratic equation by the factorisation method:
`3sqrt(2)x^2 - 5x - sqrt(2) = 0`
