Question

The area of a rhombus is equal to the area of a triangle whose base and corresponding altitude
are 30 cm and 16 cm, respectively. If one of the diagonals of the rhombus is 20 cm, find the
length of the other diagonal.

Quality answer needed ✅
​

Answer 1

$\sf\huge {\pink {\underline {\underline {Given}}}}$

• Area of Rhombus = Area of Triangle.
• Base = 30 cm
• Height = 16 cm
• One of the Diagonals of Rhombus = 20 cm

______________________________

$\sf\huge {\green {\underline {\underline {To\:Find}}}}$

• The length of the other diagonal

______________________________

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

Since we know the area of triangle and rhombus is equal

we will recall the formula to obtain the area of triangle and rhombus respectively.

Area of Triangle

${\sf⇒ \frac{1}{2} \times Base\times Height}$

Area of Rhombus

$\sf⇒ Diagonal\ 1\times Diagonal \ 2\times \frac{1}{2}Diagonal$

Here let us consider the Diagonal 2 to be 'x'.

Now let's solve an equation to find the value of d₂

$⇒ \dfrac{1}{2} \times 30 \times 16 = \dfrac{1}{2} \times 20 \times x$

Let's multiply and bring the equation to simpler form.

$⇒ \dfrac{1}{2} \times 480 = \dfrac{1}{2} \times 20x$

$⇒ \dfrac{1}{2\div 2 } \times 480\div 2 = \dfrac{1}{2} \times 20x$

$⇒ 240 = \dfrac{1}{2} \times 20x$

$⇒ 240 = \dfrac{1}{2\div 2 } \times 20$

$⇒ 240 = 10x$

Now we will flip the equation.

⇒ 10x=240

Now we shall divide 10 from both sides of the equation.

$⇒ \dfrac{10x}{10} =\dfrac{240}{10}$

⇒ x = 24x=24

${\boxed {\pink{\sf{\underline {∴ The\: length\: of\: the \:other\: diagonal\: is \:24 cm}}}}}$

____________________________________

Answer 2

Answer:

First calculate the area of the given triangle using the formula-1/2×base×height.The area would be 240 cm2. And as the area of the rhombus and triangle are same,so area of rhombus =240cm2. Now that we've got the area, it is given that the length of one diagonal of the rhombus is 20 cm,so we can now easily find out the other diagonal as well by this formula-Area of rhombus =1/2×(diagonal 1×diagonal 2) If we put the values and solve the equation,we will get 6 as the answer. Happy to help!