1. A box is (2x - 3) by (x + 5) by ( 3x + 1), what is the volume of the box if x = 3 cm?
2. The formula for the area of a triangle is A = If the base (b) = 10 cm and the height (h) = 6 cm,
what is the area of the triangle?
3. The length () of the rectangle is x2 + 2x - 3 and the width (w) is 5x + 4, what is the perimeter of
the rectangle?
4. From the sum of 3x3 + 7x2 5 and 2x2 + 3x + 8 take away 5x2 + x - 5.
5. What should be added to 3x3 + 4x2 - 7 to have a sum of 4x3 + x2 + 5.
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Answer:
If a,b,c are the sides of a triangle , then according to Hero's Formula area of triangle is
s(s−a)(s−b)(s−c)
where s=
2
a+b+c
For the given triangle,
s=
2
x+x+1+2x−1
=
2
4x
=2x
Area =x
10
2x(2x−x)(2x−x−1)(2x−2x+1)
=x
10
2x(x)(x−1)(1)
=x
10
x
2(x−1)
=x
10
2(x−1)
=
10
⇒2(x−1)=10
x−1=5
x=6
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