Question

find the length of the diagonal, if the area of the quadrilateral PQRS is 60 cm².​

Answer 1

$\LARGE{ \underline{ \underline{ \purple{ \bf{Required \: answer:}}}}}$

► GiveN:

• Perpendicular from R to diagonal QS = 4 cm
• Perpendicular from P to diagonal QS = 6 cm
• Area of the quadrilateral = 60 cm²

► To FinD:

• Find the length of the diagonal QS....?

How to solve?

Here, area of the quadrilateral is the sum total of area of the two triangles. And, we know the height of these triangles and base is common but it's measure is unknown. So, we can form an equation and get the required result.

Working out:

We have,

• Area of the quadrilateral = 60 cm²

Area of the quadrilateral PQRS = Area of triangle QRS + Area of triangle PQS.

Formula to find area:

$\large{ \boxed{ \rm{Area \: of \: \triangle = \frac{1}{2} \times base \times height}}}$

So,

➝ Area of PQRS = Area of △QRS + Area of △PQS

➝ Area of PQRS = 1/2 × RT × QS + 1/2 × PU × QS

➝ Area of PQRS = 1/2 QS (RT + PU)

Putting the values given in Q.

➝ 60 cm² = 1/2 QS (4 cm + 6 cm)

➝ 60 cm² = 1/2 × 10 cm × QS

➝ 60 cm² = 5 cm × QS

➝ QS = 60 cm² / 5 cm

➝ QS = 12 cm

Final result:

• Length of the diagonal QS = 12 cm.

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Answer 2

Question:-

Find the length of the diagonal, if the area of the quadrilateral PQRS is 60 cm²

Formula Used:-

Area of a triangle = 1/2 * base * height

Answer:-

Area of □QPSR = Area of △QPS + Area of △QRS

➨ 60 = ( 1/2 * PU * QS) + ( 1/2 * RT * QS)

➨ 60 = ( 1/2 * 6 * QS ) + ( 1/2 * 4 * QS)

➨ 60 = 3QS + 2QS

➨ 60 = 5QS

➨ QS = 60/5 cm

➨ QS = 12 cm

Ans. QS = 12 cm