Question

the area of a rhombus is 144 cm2 and one of its diagonals of double the other. the length of the longer diagonal is

Answer 1

Answer:

Area of rhombus = 144 cm square

One of its diagonal is double the other

let diagonal 1 (d1) be 'x '

(according to the question )

One of the diagonal is double than other

So,

diagonal 2(d2) = 2x

\begin{gathered}\bf area \: of \: rhombus = \frac{1}{2} \times d1 \times \: d 2 \\ \\ = 144 = \frac{1}{2} \times x \times 2x \\ \\ = 144 = \frac{ {2x}^{2} }{2} \\ \\ = 144 = {x}^{2} \\ \\ = \sqrt{144} = x \\ \\ = 12 = x\end{gathered}

areaofrhombus=

2

1

×d1×d2

=144=

2

1

×x×2x

=144=

2

2x

2

=144=x

2

=

144

=x

=12=x

diagonal 1 = x = 12 cm

diagonal 2 = 2x = 2 × 12 = 24 cm

CHECK

area of rhombus

\begin{gathered}\bf = \frac{1}{2} \times d1 \times d2 \\ \\ = \frac{1}{2} \times 12 \times 24 \\ \\ = 6 \times 24 \\ \\ = 144 {cm}^{2}\end{gathered}

=

2

1

×d1×d2

=

2

1

×12×24

=6×24

=144cm

2