Question

One side of a kite is 8 cm less than four times the length of another side. The perimeter of the kite is 78 cm. Find the lengths of the sides of the kite

Answer 1

`9.4\:\mathrm{cm},\\9.4\:\mathrm{cm},\\29.6\:\mathrm{cm},\\29.6\:\mathrm{cm}`

Explanation:

A kite consists of two pairs of congruent adjacent sides. Therefore, we have the following equation:

`2x+2(4x-8)=78`, where
`x` is the length of the shorter sides.

Solving, we get:

`2x+8x-16=78,\\10x=94,\\x=\fbox{$9.4\:\mathrm{cm}$}`.

Plugging in
`x=9.4` into
`4x-8`, we get:

`4(9.4)-8,\\37.6-8,\\\fbox{$29.6\:\mathrm{cm}$}`.

Therefore, two sides have length
`9.4\:\mathrm{cm}` and two sides have length
`29.6\:\mathrm{cm}`.