Question

If in a parallelogram PQRS,
PQ = 6x+7
QR = 3x+5
RS = 2y+5 and
PS = 3y-6.
then, what is PQ : PS?​

Answer 1

Step-by-step explanation:

here is your explanation!!

Answer 2

PQ : PS = 5:3.

• A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
• A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base (one of the parallel sides) and height (the distance from top to bottom) of the parallelogram determine its area. A parallelogram's perimeter is determined by the lengths of its four sides. The qualities of a parallelogram are shared by the shapes of a square and a rectangle.
• A parallelogram is a rhombus if all of its sides are equal to one another or congruent. A trapezium is a shape that has one parallel side and two non-parallel sides.

Here, according to the given information, we are given that,

PQ = 6x+7 and RS = 2y+5.

Now, we know that, opposite sides are equal in a parallelogram.

Then, we get,

$6x+7 = 2y+5.$

Or, x = $\frac{2y-2}{6}$

Or, x = $\frac{y-1}{3}$.

Also, we have, 3x+5 = $y-1+5=y+4.$

Now, $y+4=3y-6.$

Or, $2y=10$

Or, y = 5.

Then, RS = $2.5+5 = 15.$

Then, PQ = 15.

PS = 15 - 6 = 9.

Hence, PQ : PS = $\frac{15}{9} = 5:3.$

Hence, PQ : PS = 5:3.

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