Question

Ashok wanted to divide his rectangular field to grow flowering plants for his flower
business. He wanted to divide the field into four triangular parts as given in the figure
below.
In the field ABCD, E and 0 are the mid points of AB and BD respectively.
Given AB =400m and AD =480 m.
480 m
D
400 m
'C с
(a) Find the length of the side DE of AADE.
(i) 520 m
(ii) 670m
(iii)650m
(iv) 580m​

Answer 1

Given:

Ashok wanted to divide his rectangular field to grow flowering plants for his flower business. He wanted to divide the field into four triangular parts as given in the figure below.

In the field ABCD, E and 0 are the midpoints of AB and BD respectively.

Given AB = 400m and AD = 480 m

To find:

The length of the side DE of ΔADE

Solution:

Referring to the figure attached below, we have

The dimensions of the field ABCD:

Length AB = 400 m

Breadth AD = 480 m

∵ E is the midpoint of AB

∴ AE = $\frac{1}{2} \times AB = \frac{1}{2} \times 400 = 200 \:m$

Considering Δ ADE, using the Pythagoras theorem, we get

$DE^2 = AE^2 + AD^2$

$\implies DE = \sqrt{ AE^2 + AD^2}$

$\implies DE = \sqrt{200 ^2 + 480^2}$

$\implies DE = \sqrt{40000 + 230400}$

$\implies DE = \sqrt{270400}$

$\implies \bold{DE = 520\: m}$

Thus, the length of the side DE of ΔADE is → option (i) → 520 m.

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