Answer :

Let us consider a Rectangular yard **ABCD**,

According to the problem, it is given that

Δ**ADF**, Δ**BCE** are a congruent isosceles right triangle.

It is also given that,

Length of **AB** is **25**m.

Length of **BC** is **15**m.

From the figure, we can clearly say that,

**AB = DF + FE + EC** and

**DF = EC**.

From the above equations and data are given in the problem,

⇒ 25 = (2 × DF) + 15

⇒ 2 × DF = 25 - 15

⇒ 2 × DF = 10

⇒

⇒ **DF = 5**m

From isosceles right triangle **ADF**,

We can see that **AD = DF**,

So breath of Rectangle **ABCD** is **5**m.

We know that Area of Rectangle = Length × Breadth

From the figure and calculations, we can clearly say,

Length of Rectangle **ABCD** is **25**m.

The breadth of Rectangle **ABCD** is **5**m.

The base of Triangle **ADF** is **5**m.

The height of Triangle **ADF** is **5**m.

Area of Rectangle ABCD = 25 × 5

**Area of Rectangle ABCD = 125**m^{2}.

Area of Triangle

Area of Triangle

**Area of Triangle ADF = 12.5**m^{2}

The area in the Rectangular yard that containing flower beds is the area of two Triangles **ADF** and **BCE**.

But according to the problem, it is told that **ΔADF** and **ΔBCE** are congruent.

So, the area of both the triangles is the same.

Area of **ΔADF** = Area of **ΔBCE** = **12.5**m^{2}.

The area occupies by flower beds = Area of **ΔADF** + Area of **ΔBCE**.

The area occupies by flower beds = 12.5 + 12.5

The area occupies by flower beds = **25**m^{2}.

The fraction(**f**) of the yard that is occupied by the flower bed is given by

⇒

⇒

The fraction is .

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