Question

7«. Triangle ABC is an equilateral triangle. Point P is on base BC such that PC = 1/3BC,
if AB = 6 cm find AP.

Answer 1

Hey

Here is your answer,

In attachment

Hope it helps you!

Answer 2

∆ABC is an equilateral triangle,
i.e. Its all sides are equal
& all angles are 60° each.

Given : PC = ⅓BC i.e. 3PC = BC,
AB = 6 cm. AR is the altitude .

To Find : AP

Solution :

AB = BC = AC = 6 cm .....( Sides of equilateral are equal )
PC = ⅓BC = ⅓×6 = 2cm

RC = ½BC ... [ altitude of an equilateral triangle is the itself median ]
RC = ½6 = 3 cm
RP = RC - PC = 3 - 2 = 1 cm

In ∆ARC, AR = √3/2×AC .. (side opposite to 60°)
.°. AR = √3/2×6 = 3√3 cm.

In ∆ARP, By the Pythagoras theorem,
.°. AP² = AR²+RP²
.°. AP² = (3√3)²+(1)²
.°. AP² = (9×3) + 1
.°. AP² = 27 + 1
.°. AP² = 28
.°. AP = √(7×4)
.°. AP = 2√7 cm

@Jayesh ! ✌