Question

Example 2: The area of a rhombus is 240 cm’ and one of the diagonals is 16 cm. Find
the other diagonal.​

Answer 1

Given

Area of rhombus is 240cm²

One of the diagonal is 16cm

To Find

length of other diagonal

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Let us assume that the x and y be the two diagonals of the rhombus

$\sf \large\boxed{\: Area \: of \: Rhombus = \frac{D_{1 }\times D_{2}}{2}}$

$Area \: of \: Rhombus = \dfrac{xy}{2}$

$\sf \longmapsto240 = \dfrac{16 \times y}{2}$

$\sf \longmapsto16y = 240 \times 2$

$\sf \longmapsto16y = 480$

$\sf y = \dfrac{480}{16} = 30$

∴Length of other diagonal is 30cm

Check:-

Area of rhombus=30×16/2

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$=480/2

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$=240cm²

Extra information=>

• All sides of rhombus are equal and opposite sides are parallel.
• Diagonals of Rhombus bisects each other at 90°.
• There are four congruent right angled triangles formed between the two diagonals.

Answer 2

Answer:

15 cm

Step-by-step explanation:

Area of rhombus = 240 sq cm

Length of one diagonal = 16 cm

Let the length of other diagonal be x cm

As we know, area of rhombus = product of diagonals

240 = 16*x

240\16 = x

15 cm = x

Hence the length of other diagonal is 15 cm