Advertisements
Advertisements
प्रश्न
In the given figure, the perimeter of parallelogram PQRS is 42 cm. Find the lengths of PQ and PS.
Advertisements
उत्तर
Area of ||gm PQRS = PQ x 6
Also,
Area of ||gm PQRS = PS x 8
∴ PQ x 6 = PS x 8
⇒ PQ = `(8"PS")/(6)`
⇒ PQ = `(4"PS")/(3)` ....(i)
Perimeter of ||gm PQRS = PQ + OR + RS + PS
⇒ 42 = 2PQ + 2PS ...(opposite sides of a parallelogram are equal)
⇒ 21 = PQ + PS
⇒ `(4"PS")/(3) + "PS"` = 21 ...[From (i)]
⇒ `(4"PS" + 3"PS")/(3)`
⇒ 7PS = 63
⇒ PS = 9cm
Now,
PQ = `(4"PS")/(3)`
= `(4 xx 9)/(3)`
= 12cm
∴ PQ = 12cm and PS = 9cm.
APPEARS IN
संबंधित प्रश्न
E is the mid-point of side AB and F is the mid-point of side DC of parallelogram ABCD. Prove that AEFD is a parallelogram.
The alongside figure shows a parallelogram ABCD in which AE = EF = FC.
Prove that:
- DE is parallel to FB
- DE = FB
- DEBF is a parallelogram.
In the alongside diagram, ABCD is a parallelogram in which AP bisects angle A and BQ bisects angle B.
Prove that:
- AQ = BP
- PQ = CD
- ABPQ is a parallelogram.
PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.
Prove that: RT bisects angle R
PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.
Prove that: ∠RTS = 90°
In a parallelogram ABCD, E is the midpoint of AB and DE bisects angle D. Prove that: BC = BE.
In the Figure, ABCD is a rectangle and EFGH is a parallelogram. Using the measurements given in the figure, what is the length d of the segment that is perpendicular to `bar("HE")` and `bar("FG")`?
Which of the following statement is correct?
In the following figure, it is given that BDEF and FDCE are parallelograms. Can you say that BD = CD? Why or why not?
Construct a parallelogram POUR in which, PO = 5.5 cm, OU = 7.2 cm and ∠O = 70°.
