Question

ABCD is a square f is the midpoint of Ab BC is 1 by 3 of BC area of the triangle FBE is 108 metre square find AC​

Answer 1

Correct Question:

ABCD is a square. F is the midpoint of AB. BF is 1/3 of BC. Area of the triangle FBE is 108 metre square. Find AC

Answer:

36√2 m

Step-by-step explanation:

Let the side of the square be x m

So, AB = BC = DC = AB = x m

F is the midpoint of AB

=> AF = FB = AB / 2 = x / 2 m

BF is 1/3 of BC

=> BF = 1/3 × BC = x / 3 m

Area of the Δ FBE = 108 m²

=> 1/2 × Base × Height = 108 m²

=> 1/2 × FB × BF = 108 m²

=> 1/2 × ( x / 2 ) × ( x / 3 ) = 108 m²

=> x² / 12 = 180

=> x² = 108 × 12

=> x² = 1296

=> x = √1296

=> x = 36

Now we will find the length of BC

Consider ΔABC

∠B = 90° ( angle in a square)

So, ΔABC is a Right triangle

By Pythagoras theorem

=> AC² = AB² + BC²

=> AC² = x² + x²

=> AC² = 2x²

=> AC = x√2

=> AC = 36√2

Therefore the length of AC is 36√2 m.