In the adjoining figure,
Point S on the side PR of triangle PMR
such that 3SR = 2SP, seg ST Il side PM.
IF A ( triangle PMR) = 50 cm^2 then find
i) A( triangle RST) ii) A( quadrilateral PMTS)
Pls ans it fast.. I will mark you as a brainlist
Answers
(i) A( triangle RST) is 8 cm².
(ii) A( quadrilateral PMTS) is 42 cm².
Step-by-step explanation:
It is given that,
Point S is on the side PR of triangle PMR such that
3SR = 2SP
⇒ SR/SP = 2/3 ……. (i)
Seg ST // Seg PM
Area (triangle PMR) = 50 cm² …. (ii)
Case (i): Finding the area of triangle RST
Consider ∆RST and ∆PRM, we get
∠R = ∠R ….. [common angle]
∠RST = ∠RPM ……. [corresponding angles]
∴ By AA similarity, ∆RST ~ ∆PRM
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
∴ [Area(∆RST)] / [Area(∆PRM)] = [RS²] / [PR²]
⇒ [Area(∆RST)] / [Area(∆PMR)] = [SR²] / [(SR + SP)²]
Substituting the values from (i) & (ii)
⇒ [Area(∆RST)] / [50] = [2²] / [(2 + 3)²]
⇒ [Area(∆RST)] / [50] = [4] / [25]
⇒ [Area(∆RST)] = [4/25] * 50
⇒ [Area(∆RST)] = 8 cm²
Case (ii): Finding the area of quadrilateral PMTS
The area of quadrilateral PMTS is given by,
= [Area of triangle PMR] – [Area of triangle RST]
= [50 cm²] – [8 cm²]
= 42 cm²
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Also View:
S t Parallel to rq ,ps = 3 cm and SR= 4 cm find the ratio of area of triangle PST to area of triangle prq
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In the figure angle PQR is equal to Angle PST equal to 90 degree PQ = 5 cm and PR = 2 cm
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Answer:
PLS mark as brainliest
Step-by-step explanation:
(i) A( triangle RST) is 8 cm?
(ii) A( quadrilateral PMTS) i
42 cm?
Step-by-step explanation: It is given that,
Point S is on the side PR of triangle PMR such that
3SR = 2SP
- SR/SP = 2/3 .... (i)
Seg ST // Seg PM
Area (triangle PMR) = 50 cm2 ... (ii)
Case (i): Finding the area of triangl RST
Consider ARST and APRM, we get
ZR = ZR . [common angle]
ZRST = ZRPM .. [corresponding angles] . By AA similarity, ARST APRM
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
: [Area(ARST)] / [Area(APRM)] = [RS] / [PR)
- [Area(ARST)] /[Area(APMR)] = [SR?]/ [(SR + SP)?] Substituting the values from (i) & (ii) - [Area(ARST)] / [50] [2']/ [(2 + 3)*] [Area(ARST)] / [50] = [4]/[25] [Area(ARST)] = [4/25] * 50 - [Area(ARST)] = 8 cm2
Case (ii): Finding the area of quadrilateral PMTS
The area of quadrilateral PMTS is given by,
= [Area of triangle PMR] - [Area of triangle RST]
= [50 cm] - [8 cm?]
= 42 cm?