Plane Geometry
- If ∆PQR and ∆LMN are similar and 3PQ = LM and MN = 9 cm, then QR is equal to :
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As per the given in question , we draw figures of two similar triangles PQR and LMN
Here , 3PQ = LM and MN = 9 cm
∆ PQR ~ ∆ LMN∴ PQ = QR LM MN ⇒ PQ = QR 3PQ 9
Correct Option: D
As per the given in question , we draw figures of two similar triangles PQR and LMN
Here , 3PQ = LM and MN = 9 cm
∆ PQR ~ ∆ LMN∴ PQ = QR LM MN ⇒ PQ = QR 3PQ 9 ⇒QR = 1 × 9 = 3 cm. 3
- The perimeter of two similar triangles ABC and PQR are 36 cms and 24 cms respectively. If PQ = 10 cm then the length of AB is
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Given that , The perimeter of two triangles ABC and PQR are 36 cms and 24 cms. and PQ = 10 cm
∆ ABC ~ ∆ PQR∴ AB = BC = AC PQ QR PR = AB + BC + AC PQ + QR + PR ⇒ AB = 36 ⇒ AB = 3 PQ 24 10 2
Correct Option: C
Given that , The perimeter of two triangles ABC and PQR are 36 cms and 24 cms. and PQ = 10 cm
∆ ABC ~ ∆ PQR∴ AB = BC = AC PQ QR PR = AB + BC + AC PQ + QR + PR ⇒ AB = 36 ⇒ AB = 3 PQ 24 10 2 ⇒ AB = 3 × 10 = 15 cm. 2
- Which of the following is a true statement?
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If the corresponding sides of two triangles be proportional, the triangles are similar.
Correct Option: C
If the corresponding sides of two triangles be proportional, the triangles are similar. Hence , option C is correct answer .
- The perimeter of two similar triangles ∆ABC and ∆PQR are 60 cm and 36 cm respectively. If PQ = 18 cm, then AB is :
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Here , The perimeter of two similar triangles ∆ABC and ∆PQR are 60 cm and 36 cm
and PQ = 18 cm
∆ ABC ~ ∆ PQR
As we know that ,∴ AB = BC = CA PQ QR RP = AB + BC + CA PQ + QR + RP ⇒ AB = 60 PQ 36 ⇒ AB = 60 18 36
Correct Option: D
Here , The perimeter of two similar triangles ∆ABC and ∆PQR are 60 cm and 36 cm
and PQ = 18 cm
∆ ABC ~ ∆ PQR
As we know that ,∴ AB = BC = CA PQ QR RP = AB + BC + CA PQ + QR + RP ⇒ AB = 60 PQ 36 ⇒ AB = 60 18 36 ⇒ AB = 60 × 18 = 30 cm. 36
- Q is a point in the interior of a rectangle ABCD. If QA = 3 cm, QB = 4 cm and QC = 5 cm, then the length of QD (in cm) is
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According to question , we draw a figure of rectangle ABCD
Given that , QA = 3 cm, QB = 4 cm and QC = 5 cm,
Using Pythagoras theorem,
QD² + QB² = QA² + QC²
⇒ QD² + 16 = 9 + 25
⇒ QD² = 34 – 16 = 18Correct Option: A
According to question , we draw a figure of rectangle ABCD
Given that , QA = 3 cm, QB = 4 cm and QC = 5 cm,
Using Pythagoras theorem,
QD² + QB² = QA² + QC²
⇒ QD² + 16 = 9 + 25
⇒ QD² = 34 – 16 = 18
⇒ QD = √18 = 3√2 cm
