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Quadratic Equations

Short Answer Type

231. The age of father is equal to the square of the age of his son. The sum of the age of father and five times the age of the son is 66 years. Find their ages.

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232. The product of Shikha’s age five years ago and her age 8 years later is 30, her age at both times being given in years. Find her present age.

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Long Answer Type

233. Anita is x years old while her mother Mrs. Veena is x² years old. 5 years hence Mrs. Veena will be three times as old as Anita. Find their present ages.

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234. The difference of mother's age and her daughter's age is 21 yrs. and the twelfth part of the product of their age is less than the mother's age by 18 years. Find their ages.

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Short Answer Type

235. A rectangular field is 16 m long and 10 m wide. There is a path of uniform width all around it, having an area of 120 sq. m. Find the width of the path.

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236. The perimeter of a right-angled is Five times the length of its shortest side. The numerical value of the area of the triangle is 15 times the numerical value of the length of the shortest side. Find the lengths of the three sides of the triangle.

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237. Nine times the side of one square exceeds the perimeter of a second square by one metre and six times the area of the second square exceeds twenty-nine times the area of the First by one square metre. Find the side of each square.

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238. A retangular plot is 30 m by 20 m. It has a path of uniform width all around the plot and inside it. If the area of the path is 264 sq. m, Find the width of the path.

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239. The length of the hypotenuse of a right triangle exceeds the length of its one side by 2 cm and exceeds twice the length of the other side by 1 cm. Find the length of each side of the triangle.

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Long Answer Type

240.
In a right angled triangle, the largest side is 1 cm more than two times its shortest sides; whereas the other side is 1 cm less than two times the shortest side. Taking the shortest side to be x cm; find (in terms of x) the lengths of other sides of the triangle. Now, find:
(i) the value of x (ii) lengths of the sides of the triangle (iii) area of the triangle.

Solution not provided.
Ans. (2x+1) cm, (2x - 1) cm (i) 8, (ii) 8 cm, 15 cm, 17 cm, (iii) 60 cm²

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