Question

HELP PLEASE!!!!!!!

Reema has a piece of land which is in the shape of a rhombus . She wants her daughter  and son to work on the land and produce different crops. She divided the land in two equal parts. If the perimeter of the land is 360 m and one of the diagonal is 140 m, How much area  each of them will get for their crops?​

Answer 1

Answer:

Each of them will get 400√10 cm² of area

Explanation:

Given,

Seema divides her rhombus shaped piece of land to her daughter and son in two equal parts.

We need to find the area each of them will get.

We know,

Perimeter of a rhombus = 4 × side.

We are given with,

• perimeter = 360m.

Then,

→ 360 = 4 × side.

→ 360/4 = side.

→ 90 = side.

∴ Each side of the rhombus is 90m.

Now,

Since, the rhombus is divided into two equal parts by a diagonal. We'll get two equal triangular parts.

Area of a triangle :-

$\rm = \sqrt{s(s - a)(s - b)(s - c)}$

Where, s denotes the semi-perimeter,

a, b, and c are sides of the triangle :- 90, 90, and 140(diagonal) respectively.

Finding ‘s’ :-

→ s = [a + b + c]/2

→ s = [90 + 90 + 140]/2

→ s = 320/2

→ s = 160m

Finding area :-

$\rm = \sqrt{s(s - a)(s - b)(s - c)}$

${ = \sqrt{160(160 - 90)(160 - 90)(160 - 140)} }$

$= \sqrt{160(50)(50)(20)}$

$= \sqrt{3200 \times 50 \times 50}$

$= \sqrt{8 \times 8 \times 10 \times 50 \times 50}$

$= 400 \sqrt{10}$

∴ Each child will get 400√10m² of area.