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

Answer:

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

Step-by-step 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 $29.6\:\mathrm{cm}$.