Page 53 - Maths Skills - 7
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Simple Equations                                                                                        51

                                                    2       Example 6:  In an isosceles triangle, the base angles are
                         Multiplying both the sides by  5                  equal, the vertex angle is 50°. What are the

                                                                           base angles?
                                                2
                                      2  ×  5x   =   ×  25
                                      5    2    5    2      Solution:      Let, the base angle = x
                       or                   x  = 5                         According to the question:

                        So, Anwar thinks of 5.                             2x + 50° = 180°     [Q Sum of angles of a
                                                                                                   triangle is 180°]
        Example 5:  Father’s age is three times his son’s
                       age  and  sum of their  ages  is 100.               ⇒  2x = 130°
                       Find son’s age.                                     ⇒  x = 65°
        Solution:      Let, son is x years.                                So, base angle is 65°.
                       Then, father’s age is 3x.
                       According to question,
                            3x + x = 4x = 100
                       ⇒     x = 25
                       So, son’s age is 25 years.





                                                    Exercise 3.4



          1.  Set up equations and then solve them to find the unknown numbers in the following cases:

             (i)  Find a number which when added to its half gives 42.

            (ii)  Add 7 to 6 times a number, you get 73.

            (iii)  One-sixth of a number minus 5 gives 31.

            (iv)  Seven taken away from twice a number is 27.

          2.  Perimeter of a rectangular plot is 860 m. Its length is 4 more than its breadth. Find its length and
            breadth.

          3.  Divide 64 into two parts such that one part is 3 times the other.

          4.  In a cricket match, Arjun scored thrice as many runs as Lalit. Together they fell short of 8 runs of triple
            century. Find their scores.

          5.  A number consists of two digits. The digit at the ones place is 3 times the digit at the tens place. If 36 is
            added to the number, the digits are reversed. Find the number.
          6.  In an isosceles triangle, the base angles are equal and the vertex angle is twice the base angle. Find the
            measure of each angle. What type of triangle is it?

          7.  A sum of ` 1000 is in the form of denominations of ` 10 and ` 50. If the total number of notes is 60, find
            the number of notes of each type.
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