Question

In triangle ABC XY is parallel to BC AX = P - 3 BX = 2P - 2 AY = 1 CY = 4 then find the value of P

Answer 1

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Answer 2

Answer:

The value of P is 5.

Step-by-step explanation:

Given information: XY║BC, AX = P - 3, BX = 2P - 2, AY = 1, CY = 4.

Triangle Proportionality Theorem: If a intersect two sides of a triangle and parallel to third, then it divides those sides proportionally.

Using Triangle Proportionality Theorem, we get

$\frac{AX}{XB}=\frac{AY}{YC}$

Substitute the given values.

$\frac{P-3}{2P-2}=\frac{1}{4}$

On cross multiplication we get

$4(P-3)=1(2P-2)$

$4P-12=2P-2$

Isolate the variable terms.

$4P-2P=12-2$

$2P=10$

Divide both sides by 2.

$P=\frac{10}{2}$

$P=5$

Therefore the value of P is 5.