Question

The sides of are p , q and r. If p + q = 45, q + r =40 and p + r = 35, then find the area of the
triangle.

Answer 1

p+q=45

r+q=40

By subtracting ,

p-r=5

p+q=45

p+r=35

By substracting , we get

q-r=10 —(2)

r+q=40

-r+q=10 from 2

By substracting we get

q=25

r=15 by putting q=25 in other equation

p=20

By using heron's formula s=30

√(s-p)(s-q)(s-r)

We get answer 150

Area of triangle is 150 sq. Unit

Answer 2

Given,

p, q, and r are the sides of a triangle.

p + q = 45, q + r =40 and p + r = 35

To find,

The area of the triangle.

Solution,

The area of the triangle will be 150 units².

We can easily solve this problem by following the given steps.

According to the question,

p, q, and r are the sides of a triangle.

p + q = 45, q + r =40 and p + r = 35

Now, we will find the value of p and r in terms of q.

p+q = 45

p = (45-q) ---(1)

q+r = 40

r = (40-q) --- (2)

Now, putting these values in the following expression:

p+r = 35

45-q+40-q = 35

85-2q = 35

-2q = 35-85

-2q = -50

q = 50/2

q = 25 units

Putting the value of q in equation 1,

p = (45-q)

p = (45-25) units

p = 20 units

Now, putting the value of q in equation 2,

r = (40-q)

r = (40-25) units

r = 15 units

Now, we have the values of the three sides. We can find its area using Heron's formula:

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

where 's' is the semi-perimeter of the triangles and a, b, and c are the three sides of the triangle.

In this case, a, b and c are p, q and r respectively.

's' = p+q+r/2

's' = (20+25+15)/2

's' = 60/2 units

's' = 30 units

A = $\sqrt{30(30 - 20)(30 - 25)(30 - 15)}$

A = $\sqrt{30(10)(5)(15)}$

A = √22500

A = 150 units²

A = 150 units²

Hence, the area of the triangle is 150 units².