Two sides of a triangular field are 85m and 154m in length and its perimeter is 324m. Find
(i) the area of the field and
(ii) the length of the perpendicular from the opposite vertex on the side measuring 154m.

Question

Filo · Accepted Answer

It is given that two sides of a triangular field are 85m and 154m

Consider the third side as x m

It is given that the perimeter

= 324 m

We can write it as

85 + 154 + x = 324

On further calculation we get

x = 324 - 85 - 154

By subtraction

x = 85 m

Consider

a = 85 m, b = 154 man d c = 85 m

We know that

S = \frac{a + b + c}{2}

S = \frac{85 + 154 + 85}{2}

By division

S = 162 m

We know that

Area

s (s - a) (s - b) (s - c)

By substituting the values

Area=

162 (162 - 85) (162 - 154) (162 - 85)

So we get

Area=

162 \times 77 \times 8 \times 77

It can be written as

Area=

2 \times 9 \times 9 \times 7 \times 11 \times 2 \times 2 \times 2 \times 7 \times 11

On further calculation

Area=

11 \times 11 \times 9 \times 9 \times 7 \times 7 \times 2 \times 2 \times 2 \times 2

We get

Area=

11 \times 9 \times 7 \times 2 \times 2

By multiplication

Area=

2772 m^{2}

We know that

Area of the triangle =

1/2 \times b \times h

By substituting the values

1/2 \times 154 \times h = 2772

On further calculation

77 \times h = 2772

So we get

h = 2772/77

By division

h = 36 m

Therefore, area of the field is

2772 m^{2}

and the length of the perpendicular from the opposite vertex on the side measuring

154 m

is

36 m .

Question Text	Two sides of a triangular field are 85m and 154m in length and its perimeter is 324m. Find (i) the area of the field and (ii) the length of the perpendicular from the opposite vertex on the side measuring 154m.
Answer Type	Text solution:1
Upvotes	166

Two sides of a triangular field are 85m and 154m in length and its perimeter is 324m. Find
(i) the area of the field and
(ii) the length of the perpendicular from the opposite vertex on the side measuring 154m.

Text solutionVerified

Practice questions from similar books

Two sides of a triangular field are 85m and 154m in length and its perimeter is 324m. Find(i) the area of the field and(ii) the length of the perpendicular from the opposite vertex on the side measuring 154m.

Text solutionVerified

Practice questions from similar books

Two sides of a triangular field are 85m and 154m in length and its perimeter is 324m. Find
(i) the area of the field and
(ii) the length of the perpendicular from the opposite vertex on the side measuring 154m.