Question

. PS bisects angle QPR and PS is perpendicular to QR. If PQ = 2x
units, PR = (3y + 8) units, QS = x units and
SR = 2y units. Find the values of x and y.​

Answer 1

Given:

PS bisects angle QPR and PS is perpendicular to QR. If PQ = 2x units, PR = (3y + 8) units, QS = x units and SR = 2y units. Find the values of x and y.​

To find:

The values of x and y

Solution:

PS bisects ∠QPR . . . (given)

∴ ∠QPS = ∠RPS . . . (1)

PS is perpendicular to QR

∴ ∠PSQ = ∠PSR = 90° . . . (2)

In Δ PQS and Δ PRS, we get

∠QPS = ∠RPS . . . [from (1)]

PS = PS . . . [common side to both the triangles]

∠PSQ = ∠PSR = 90° . . . [from (2)]

∴  Δ PQS ≅ Δ PRS . . . [by ASA congruency]

We know that,

If two triangles are congruent to each other, then all 3 sides will have equal length and all 3 angles will have equal measurements.

∵ Δ PQS ≅ Δ PRS, so, we get:

$\bigg{\star}$ QS = SR

on substituting the given values

⇒ x = 2y . . . (3)

and

$\big{\star}$ PQ = PR

on substituting the given values

⇒ 2x = 3y + 8

on substituting from (3)

⇒ 2 × 2y = 3y + 8

⇒ 4y = 3y + 8

⇒ 4y - 3y = 8

⇒ y = 8

On substituting the value of y = 8 in (3), we get

x = 2y = 2 × 8 = 16

Thus, the values of x and y are:

$\boxed{\boxed{\bold{x = \underline{16\:units}}}}\\\\\boxed{\boxed{\bold{y = \underline{8\:units}}}}$

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Also View:

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Answer 2

Answer:

pls pehla aa likho

photosynthesis is a process in which green plants make their own food in presence of water sunlight and chlorophyl.

usto baad jo oehna oh likho pls