in the figure,AP:PC=3:4,BM:MP=3:2 and BQ=12cm find 4/7×AQ.
Answers
Answer:
4/7 × AQ = 8 cm
Step-by-step explanation:
Given: BQ = 12 cm
Construction: Extend P to meet AQ in Z such that,
PZ || CQ
So, AQ = AZ + QZ
So, AQ = AZ + QZ
In △PZB,
We have, PZ || QM,
By Basic proportionality theorem,
BM / MP = BQ / QZ
We can understand from the question,
BM : MP = 3 : 2
And, BQ = 12 cm
BM / MP = BQ / QZ
QZ = 12 * 2 / 3
QZ = 24 / 3
QZ = 8 cm
In △AQC,
We have PZ || QC,
By Basic proportionality theorem,
AZ / QZ = AP / PC
From the question we know that,
AP : PC = 3 : 4
We already found QZ = 8cm.
AZ / QZ = AP / PC
AZ/8 = 3/4
AZ = 3/4 * 8
AZ = 6 cm
Now adding,
AQ = AZ + QZ = 6 + 8 = 14 cm
We need to find:
=> 4/7 × AQ
=> 4/7 * 14
=> 4 * 2
=> 8 cm
Therefore 4/7 × AQ is 8 cm.
Answer:
8 cm ( 4 / 7 × AQ = 8 cm )
Explanation:
First PZ || CQ
1) AQ = AZ
2) AQ = AZ + QZ
For Triangle PZB
→ PZ || QM
Using , theorm
→ BM / MP = BQ / QZ
Given question
→ BM : MP = 3 : 2
→ BQ = 12cm
→ BM / MP = BQ / QZ
→ QZ = 12 × 2 / 3
→ QZ = 24 / 3
→ QZ = 8 cm
For Triangle AQC
→ PZ || QC
Using ,Theorm
→ AZ / QZ = AP / PC
Given question
→ AP : PC = 3 : 4
→ QZ = 8cm
→ AZ / QZ = AP / PC
→ AZ / 8 = 3 / 4
→ AZ = 3 / 4 × 8
→ AZ = 6cm
Adding them we get:
→ AQ = AZ + QZ
→ 6 + 8 = 14 cm
Finding them we get:
→ 4 / 7 × AQ
→ 4 / 7 × 4
→ 4 × 2 = 8
→ 8cm
Therefore , 4 / 7 × AQ = 8cm.
8cm is the answer.
Property used to solve this problem