1: Use the average:
sum of base AB and height CD is 26, so their average
is 13 cm. Since AB and CD differ from each other
in length by 10 cm, each differs from their average
by 5 cm. Then AB = 13 + 5 = 18 cm and CD = 13 -
5 = 8 cm. The area of the triangle is ½ ×
18 × 8 = 72 sq cm. Then the area of the square
is 144 sq cm, the length of any one side is 12 cm
and the perimeter of the square is 48 cm.
METHOD 2: Make a table: To
find the lengths of AB and CD, create a table of
number pairs whose sum is 26. The only pair whose
difference is 10 is 18 and 8. (Or create a table
of number pairs whose difference is 10 and see which
pair also has a sum of 26.) Then proceed as above
to find the area of the triangle, followed by the
area, side-length, and perimeter of the square.
METHOD 3: Solve a simpler problem: Since
AM measures 10 more than CD, subtracting 10 from
AM gives equal lengths. Subtracting 10 also from
the sum would be twice the length of CD. 26 - 10
= 16 and 16/2 is 8. Thus CD = 8 and AB = 8 + 10
= 18 cm. Proceed as above to find the area of the
triangle, followed by the area, side-length, and
perimeter of the square.
METHOD 4: Use algebra: Let
x represent the height CD, then x + 10 represents
the length of the base AB. We are given that x +
(x + 10) = 26. Solving the equation, we have x =
8. Proceed as above.