A rhombus has diagonals of lengths 16 cm and 30 cm. Find the area of the rhombus and the length of its sides.

Given the diagonals of lengths

16 cm & 30 cm

The area of a rhombus can be calculated using the formula:

A = \$1/2 \times "Product of the diagonals"\$

Now plug the values into the formula:

⇒ A = \$1/2 times 16 times 30\$

⇒ A = 240 sq.cm

Now, to find the length of its sides, you can use the half-diagonals as the legs of the right-angled triangles.

Let a and b be the half -lengths of the diagonal:

⇒ a = \$16/2\$ = 8 cm

⇒ b = \$30/2\$ = 15 cm

Using the Pythagorean theorem in each right-angled triangle:

Side of Rhombus = \$\sqrt(a^2 + b^2)\$

Now plug the values into the formula:

⇒ S =\$\sqrt(8^2 + 15^2)\$

⇒ S = \$\sqrt(64 + 225)\$

⇒ S = \$\sqrt(289)\$

After simplification

S = 17

Hence, the area of the rhombus is 240 sq.cm, and the length of each of its sides is 17 cm.

Can you summarize what you’ve understood in the above steps?

This is correct because the area and the length of the sides match the formulas for a rhombus with diagonals of 16 cm and 30 cm

240 sq.cm and 17 cm

This is not correct because the area and the length of the sides does not match the formulas for a rhombus with diagonals of 16 cm and 30 cm

204 sq.cm and 71 cm

Incorrect answer. Units for area are different. The correct answer needs square centimeters for area, not just centimeters for side length

240 cm and 17 sq.cm

Incorrect answer. Units for area are different. The correct answer needs square centimeters for area, not just centimeters for side length

204 cm and 71 sq.cm

Option

A

Can you summarize what you’ve understood in the above steps?