Question

The area of a triangular flag is 132 square centimetres. Its altitude is 2 centimetres longer than twice its base. Find the lengths of the altitude and the base.

Answer 1

24 cm and 11 cm

Explanation:

GIVEN: The area of a triangular flag is
`132 \text{ cm}^2`. Its altitude is
`2\text{ cm}` longer than twice its base.

TO FIND: lengths of the altitude and the base.

SOLUTION:

Let the altitude and the base of flag be
`a` and
`b`

According to the question

`a=2+2b`

area of triangle
`=(1)/(2)* base * alltitude=(1)/(2)a* b`

`\implies (1)/(2)(2b+2)b=132 \Rightarrow 2b^2+2b-264`

Solving equation we get

`b=11` then
`a=24`

Hence the lengths of altitude and base of triangular flag is 24 cm and 11 cm respectively.